Here's my quick kit-bash.
Two Action Economy
5e has one action, one bonus, and a move. The move is fun. The move is life. You can move before, after, and between actions. It's so f***ing simple I would hate to change it.
So now let's combine action and bonus action. And let's apply a -5 penalty if you make second attack in the same round. (In PF2, third attacks are lame and boring; they seldom hit unless you're using a high level monster, and if you have a big nasty powerful monster, it should be doing more interesting things than just HP damage.)
You can make two attacks if you want, but we're going to give you more interesting options. For instance, maneuvers like shoving and grappling don't count as attacks, so a pretty typical fighter turn would be to attack then do a maneuver.
4e-Style Defenses
You have Reflex defense, Fortitude defense, Will defense, and Maneuver defense. If someone wants to hit you, Reflex defense. Poison? Fort. Charm? Will. Grapple/shove/disarm/reposition? Maneuver.
Armor does something new aside from increasing a defense.
PF2-Style Degrees of Success
You have success (beat the DC/Defense), critical success (beat by 10), failure (don't beat it), and mishap (miss it by 10). This is a critical game mechanic, as you'll see below.
If you crit with an attack, instead of dealing extra damage, you can inflict a wound. Usually these are 'light wounds' (which can be cured with a 1st level spell, or a short rest and medical care), but if you run out of HP, they become 'serious wounds' (which can be cured with a 3rd level spell, or a long rest with medical care). I'll explain wounds below.
If you have a mishap on an attack, the person you attacked gets to make a maneuver against you.
If you crit with a maneuver, the maneuver is more effective - shoving farther, or pinning, or knocking their sword far from their hand, etc. If you mishap on a maneuver, the person gets to attack you.
If you have a crit with a spell, often there'll be something cool. But there's a lot of variety in spells, so it's hard to simplify them.
A Suite of Saves
Here's the piece de resistance: between each short rest, a PC can use between 2 (at first level) and 6 (at high level) saves. These are abilities that downgrade the severity of an incoming attack by one step, and usually add some extra perk. You might turn a crit into a normal hit, or turn a failure into a mishap.
The Basic Combat save lets you downgrade a maneuver or weapon attack against you, and then perform a maneuver against your attacker.
The Basic Reflex save lets you downgrade any reflex attack against you, then move half your speed.
The Basic Fortitude save lets you downgrade any fortitude attack against you, then lets you ignore the effect of your wounds for a round.
The Basic Will save lets you downgrade any will attack against you, then . . . okay, I haven't figured this one out yet.
Armor grants saves too that reduce the severity of weapon attacks (and can be repaired in down time).
You might learn new saves by leveling in different classes, but you can only prepare a limited amount.
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The result is that the game encourages you to both fight and use maneuvers, and gives you a little bit of counterplay that is akin to 'parrying' an attack in a video game. I think combat would be more dynamic than 5e, and less clunky and mathematical than PF2.