Giving 2 extra levels to your characters should be fine at low level. At higher level, it may become a bit more problematic but depending on the AP you may focus only on the low level experience.
The real issue is that both characters will need to be extremely versatile to handle any kind of threat. I'd personally also add the Dual Class optional rule to give them more versatility, limiting the choices to one martial and one caster class so they will be able to handle more situations. Another solution if you don't want to add such an impactful rule is to only use Free Archetype. It will allow your players to have more versatility without impacting the balance of the game.
Anyway, even if the game should be fine with only 2 players and 2 extra levels (because PF2 is really well balanced) it will be very random as a single character rolling a natural 1 to a save may turn a simple fight into a TPK.
The biggest problem with fewer players is fewer actions each round from the party as a whole. With 4 players they have 12 actions and 4 reactions in total. With only 2 players, that is 6 actions and 2 reactions.
That needs to be corrected by adjusting the encounters. For solo or dual enemy fights, the weak template can be applied - and there is a button for that on Archives of Nethys. For battles with more enemies, simply removing one or two of them should do the job (instead of a battle against six APL-1 enemies, make it a battle against four of those same APL-1 enemies).
The next biggest problem is the amount of skills that the party will have available. With only 2 characters playing, they won't have as many trained or trained+ skills available.
The best way to fix that is with Free Archetype or maybe Dual Class. I find that Free Archetype is enough as long as the players do some metagame planning when picking skills.
I don't see the action issue as that big of a problem. It's the same issue when you put higher level enemies: They have less actions. Still, they pack their punch. I personally think the system is so solid you can do something as crazy as to put 2 level+2 characters in an AP and end up well. It can even be super fun as characters will really feel super powerful and facing extreme odds.
Reading the title, I had the same thought as SuperBidi: 2 extra levels + dual class, or at the very least free archetype, to add versatility.
I agree that only 2 players is a distinct situation where Dual-class might do well. But it wouldn't take care of things due to the action issue mentioned. The adding 2 levels may help this, but it still leaves situations that cause a stun, or other incapacitation on one player, ending up having a greater impact than probably intended.
Something to consider, might be rather than having each player playing a second player, instead have your 2 PCs with dual-class, and add one NPC, whom the two players will cooperatively be responsible for their actions. This would sort of be combining a partial #2 with #4 (which you might consider dropping to just 1 level, but for reasons I might mention later, I'd suggest keeping it at 2).
That way full responsibility doesn't fall solely on them (as individuals).
Another option would be to give them a 'Party' animal companion that will basically repeat actions if not given new orders. Giving the players an option to use their third actions to give direction and a couple actions to the 'extra'. Then a metagame rule would allow any completely incapacitated player, would get to run the companion each round as if an action had been spent to direct it. there would be a slight onus to keep the Animal Companion behaving animal-like, or at least animal like in the sense of Lassie was an 'animal' that seemed to always figure out how the help her Humans.
Also keep in mind, some of the APs have a history of being hard even for intended levels, so you might need more than 2 levels lead to be safe. This is one reason I'd suggest you keep your boost to +2 levels.
Might think about bumping number of spell slots per level by 1 to reduce the tendency to run out of daily resources. That might not be as much a problem if they double up on different spell casting classes.
I think that dual class and +1 level would be enough in general (specially if one of them goes double martial). +2 might only be necessary levels 15+. If you are ok with rebalancing encounters by removing or changing creatures late game shouldn't even be an issue (point is better reduce the amount of creatures later on than just give them extra levels).
I'd say dual class. Or, since you don't want 2 characters for RP reasons, you could explain it this way. Each has a "main." And they have two hirelings. A fighter hireling (mercenary/bodyguard) and a bard or rogue hireling. Then they could play a cleric and sorcerer for their "mains."
Controlling two NPCs would be a lot, but dual class + one NPC that mostly exists as a way to lighten up the party's resources, rather than be a direct contributor, could work. This would be a good place for a heal/buffbot that's really not particularly strong but takes some of the load off your players.
I remember seeing it suggested by one of the devs (Jason I think, but I could be wrong about who) that running 2 PCs for an AP, one should run Dual-Class +1. However, +2 shouldn’t be much issue and will probably be more fun for the players.
I agree that only 2 players is a distinct situation where Dual-class might do well. But it wouldn't take care of things due to the action issue mentioned. The adding 2 levels may help this, but it still leaves situations that cause a stun, or other incapacitation on one player, ending up having a greater impact than probably intended.
Something to consider, might be rather than having each player playing a second player, instead have your 2 PCs with dual-class, and add one NPC, whom the two players will cooperatively be responsible for their actions. This would sort of be combining a partial #2 with #4 (which you might consider dropping to just 1 level, but for reasons I might mention later, I'd suggest keeping it at 2).
That way full responsibility doesn't fall solely on them (as individuals).
Another option would be to give them a 'Party' animal companion that will basically repeat actions if not given new orders. Giving the players an option to use their third actions to give direction and a couple actions to the 'extra'. Then a metagame rule would allow any completely incapacitated player, would get to run the companion each round as if an action had been spent to direct it. there would be a slight onus to keep the Animal Companion behaving animal-like, or at least animal like in the sense of Lassie was an 'animal' that seemed to always figure out how the help her Humans.
Also keep in mind, some of the APs have a history of being hard even for intended levels, so you might need more than 2 levels lead to be safe. This is one reason I'd suggest you keep your boost to +2 levels.
Might think about bumping number of spell slots per level by 1 to reduce the tendency to run out of daily resources. That might not be as much a problem if they double up on different spell casting classes.
Losing actions to incapacitation will hurt more, but conversely the PCs should be threatened by a smaller of incapacitation effects because their relative level will be higher. Probably still a danger though for APL+2 OR +3 solo battles though.