I recently shared a lot of thoughts about this over on GFaqs, mostly mechanics focused. That thread was talking more about a sequel but I think it fits reasonably well here as well. Most of these thoughts are very similar, but I've expanded the support character section a lot since then.
1) Heavy tweaks to stats, skills and weapon balance
I won't go into detail about the problems here for those who aren't aware - but in short, a few skills for both weapons and characters dominate the game, and weapon power ends up so high that most stats just don't matter at all, making all of the individuality of each character's stats just come down to "X has higher luck than Y so X is better" if they have the same moveset, and otherwise the only relevant stat being luck.
So there's a significant number of possible changes here. I'd actually prefer to see a bit of a return to lower numbers for stats, similar to more classic FE games, but realistically that probably won't happen. So let's assume stats simply don't change much - the same kind of stat distributions happen in FEW2 as now (but no 999 HP cap as that's unnecessary).
However, to make many stats more significant, we have to tweak other mechanics, or how they work:
a) Reduce weapon might considerably. For example: Bronze as 10-15. Iron as 20-30. Steel as 40-60. Silver as 70-105. Brave as 110-165. Hero as 180-270. Personal weapons first are raised to 165 (by scroll), then to 270 (by Opus). This is high enough that having a good weapon can still have a very significant impact on damage, but allows differences in strength stats to have a realistic impact on damage. Currently, adding strength on to a 720 power weapon does basically nothing, but adding it to a 270 power weapon is far more noticeable. Obviously to accommodate this change, enemies would have to have lower HP/Def, especially later in the game, but minor changes like that are relatively easy.
b) Tweak the stat some skills run on, or make them run on several stats. Luna has always traditionally depended on skill in FE games, so why not keep it that way here when skill is a relatively less important stat? Some skills could also depend on speed, to make that more significant as well.
c) Reduce the damage limit for getting S ranks. It's a bit too easy currently, which makes defensive stats unimportant. If you had to actually pay attention to defences when picking characters, things might be a bit more balanced.
d) General rebalancing of many skills. Luna is broken in its current form, I think most people know that. I've suggested formulae for it in the past that would make it scale much less oppressively. Lethality as well. But also, bump up the effectiveness of some of those less good skills: Make the stat+10 skills instead a stat +20% (with maybe a minimum +5 bonus so they're still of use at low levels) so they're still viable even at higher levels. Some of the situational damage boosters could be larger as well, like Awakening.
2) Pair Up, Support characters and multiple weapon types
One thing that almost every FE game has, is characters who can use several weapon types. In a sense, FEW vaguely allows you to do this as you can swap characters in a pair up - but that really isn't the same thing, is it? But also with pair up existing, having several weapons on a character feels a little redundant. Fortunately, I've thought of a system that would have several benefits, which I call "Support characters", that also has many other potential benefits. I'll explain what these are first.
Support characters would replace the current pair up system, you would no longer be able to pair up two playable characters and switch the vanguard at will. Support characters would be a wide library of non-controllable characters who are optionally assigned to each character at the start of battle (or using a default from the previous battle, similar to weapons+items). Like the current pair up partners, they don't usually appear directly on the battlefield but will appear briefly for their dual action (e.g. dual strike). They cannot be dismissed to act separately, but can be swapped with another playable character's support character when nearby. A character that is normally playable can be assigned as a support, if they are not otherwise deployed in the battle. Since support characters don't fight and there would be a lot more of them than playable characters, they gain EXP at a greatly increased rate, perhaps around 3x normal character EXP gain. However their levels have relatively smaller impact.
Since support characters do not function like full characters, a lot of the work in creating them would be stripped out: They would have considerably fewer animations, only a few voice lines in battle, and only one costume. Considerably less effort to create them means you can realistically create a LOT more of them: The current game has 32 playable characters, you could realistically probably make 10+ support characters in the time it takes to fully develop just one character. And they could still be potential candidates for DLC or free updates to make them into fully fleshed out characters further down the line as well. Plus, they could still have support conversations and support levels with playable characters, potentially. Speaking of supports, to compensate for less support gain via pair up fighting, increase the amount gained by simply being deployed in the same map, and also gain support based on fighting near each other, not just while paired up.
Essentially, support characters would allow a lot of characters who may otherwise have no chance of appearing in the game get in, at the cost of perhaps a small number of full character slots. You would also have the potential to deploy up to 8 characters with pair up partners into every map, which might make the game feel a bit more like a traditional FE game with a large army of unique characters.
Speaking of pair up, the bonuses from your support character would work very differently. Every support character would still give a bonus to stats, but this bonus would be based now on the level of the support character, increased slightly by support rank you have with them. Dual Specials are gone (they're cute once or twice and the voice clips are nice, but otherwise they're OP and slow the gameplay down too much), and as for other effects, that depends heavily on the character. Increasing support level would no longer increase the rate that the dual strike/guard gauge charges, instead the single dual gauge that replaces it would always fill at a constant rate - but with higher support levels can be "overfilled" a certain amount, 1/3rd of a gauge extra per support level (meaning A support lets you double fill it, allowing e.g. two dual strikes in quick succession).
Instead of a pair up partner giving access to dual specials, dual strikes, dual guards etc., supports here would give access to one main bonus depending on the character you support. Each support character would have one of five types (along with their corresponding dual action): Attack (Dual Strike), Defence (Dual Guard), Mobility (Dual Charge), Healing (Dual Heal) and Augment (Dual Rally). Many of these are new, and even the ones that aren't need some explaining (see spoiler below)
This system would be a big difference from what we've got, but it would hopefully serve a few interesting purposes: It helps differentiate the support character from each other by varying what they can actually do, it makes choosing your support character interesting, it makes pair up somewhat less insane in power by separating out many of its potent effects and forcing you to choose just one.
Now, with pair up not letting you simply switch characters, we can move on to the next part of this thing I'd like to see: Weapon swapping, or multi-weapon wielding, or whatever you'd like to call it. After promotion, each character would get a second moveset. Yes, these would probably mostly be clones of other characters, sorry. I'd prefer two unique on everyone, sure, but that just isn't realistic. However I envision that no character would share BOTH movesets with someone else, so at least everyone would be arguably more unique than FEW? Anyway, in battle you'd have the ability to swap weapon and use your second moveset and weapon type. One downside to this might be, to force decisions on the player, your second weapon would go in the same slot as your item otherwise would. So you can bring a second weapon type, but in exchange you sacrifice the ability to heal. Additionally, some characters after promotion, such as Ryoma, may not get a second weapon type but still get an alternate moveset - in that case, they would have the option to not equip a second weapon and just use their first for both - a small advantage in terms of weapon optimising, and allowing them to keep using their item slot. Not much more to say about this, especially. Everyone would still only have one personal weapon.
3) Other miscellaneous improvements
* Improved AI commands menu
One minor frustrating thing in the game is having to constantly pause and change AI targets every time they achieve something, or just ignore the fact they could be being more helpful and simply let them roam wild. Since FE is a strategy and tactics game first and foremost, let's add a few extra options here:
a) Queue orders on a unit. Order them to kill target enemy A, then capture fort B, then guard that fort, all before even starting the mission. Now you can play missions with fewer distractions.
b) More advanced orders on units. Kill target or defend ally/fort exist, which is nice. Let's add a few others, such as patrol area, making a unit move around a designated zone and attack any enemies that come near, an interrupt to go heal option so they can do task X, but if someone ends up below half health they break off and go heal them, things like that. Also, things like attacking/defending specific outposts and the like,
c) For players who prefer to just jump right into battle without spending a minute or two crafting their strategy, orders without pausing. When an AI character finishes their order, you currently get a textbox of them basically saying they're done. Let's have that message hover with a button prompt you can hold down, to bring up a quick menu and assign a quick instruction for their next action on the fly.You could have a number of basic options from this such as "Attack nearby enemies", "Attack a nearby fort", "Come to me", "Defend your current location", "Defend the allied base" etc. Quick, simple things that don't require pausing, so you can keep the action going.
* Showing enemy stats in game. Why not? The game is already good enough to give us levels, just cut out a bit more of the guesswork.
* Movement stats that are actually proportional to movement speed. This one seems so obvious in retrospect. Flying units with 20 move are obviously not moving 4 times as fast as Infantry units with 5 move, so how about we actually just get propotional values here? For reference, the rule is roughly "add 15-16 to the move stat" if you want to compare, e.g. flyers are about 35/20 times as fast moving as infantry - so why not just show infantry as 20 move, fliers as 35 move, cavalry as 30 and Frederick as 25?
Probably a bunch of other minor stuff.