Can you use a move action to make a swift action?
What if you have 2 swift spells and a standard one, can you cast them all in one round?
If you have two swift action abilities you cannot traditionally use both in the same round unless you have some sort of Rule 0 or power from another effect that specifically allows it. I did look into Standard Action rules to see if you can use a standard action on a swift one (as sort of a downgrade as it were) but the description below clearly debunks that. So if you have two swifts and a standard, one of those swifts will just have to wait until your next turn.
According to d20PFSRD:
D20 SRD says the same but with about half the paragraph so I gave the longer answer since you tagged both 3.5e and Pathfinder.
Actions Taking More Time Can't Be Traded for Actions Taking Less Time
The action system in Dungeons and Dragons 3.5 and derivative works is strict--so strict that breaking it is often the goal of system optimizers. When a character can do more or different things with the typical allotment of actions, the universe sobs.
By default, during a turn, a creature can take 1 standard action, 1 move action, 1 swift action, 1 5-ft. step if no other movement has been used, and any number of free actions the DM permits. A full-round action can be taken instead of both 1 standard action and 1 move action. A second move action can be taken instead of a standard action (PH 138). If a creature takes an immediate action, it can't take a swift action on its next turn.
The game explains what a creature can do, not what a creature can't do unless it's clarifying, so despite the initial batch of actions taking increasingly smaller amounts of actual, character-point-of-view time, a creature without special abilities specifically allowing it to do so can't exchange a longer action for a shorter action (e.g. a creature can't take a second swift action instead of taking a move action) nor combine shorter actions to take longer ones (e.g. a creature can't shove together its 5-ft. step, its swift action, and all its free actions to take an additional standard action). That's just not a thing.
Use Tokens to Track Actions
There's more to it than this (as if this isn't complex enough already) and special circumstances abound, but this should permit muddling through.
If you find this particularly useful, I suggest adding violet tokens to each turn's pile representing the creature's number of attacks of opportunity (PH 137). Spend 1 violet token from the upcoming turn pile when a creature takes an attack of opportunity.
On your turn you'll have 2 piles of tokens--this turn's pile and the upcoming turn's pile--, with this turn's pile containing 1 red, 1 orange, 2 yellow, 1 blue, and infinite indigo tokens, but no green token because you spent that already; and the upcoming turn's pile containing 1 red, 1 orange, 2 yellow, 1 green, 1 blue, and infinite indigo tokens.
Credit Where Credit's Due: The Use Tokens for Actions idea is from somebody's blog (although these words are mine), but I can't remember whose. I'll link to it if someone finds it.
No, the only default action-trading available are standard for move, or move+standard for full-round.1 You cannot trade any other action to get more swift actions. In fact, getting more swift actions is extremely limited:
The only way in 3.5 to take more than one swift action in a turn is RKV
The ruby knight vindicator from Tome of Battle gains the ability to burn a use of Turn-or-Rebuke Undead for an extra swift action in a turn. This is literally the only option in all of 3.5 that allows more than one general-purpose swift action in a round.
This is definitely a no-no because you're technically adding actions. A Swift action is definitely more valuable than a Move Action. So 2 Swift + 1 Standard would be better.
That stated, as a Pathfinder DM if you wanted to make 2 Swift actions and 0 Standard actions, I would probably allow this. Swift actions are less powerful than Standard actions, so if you took an Immediate Action and then needed to cast a spell on your turn that had a casting time of Swift, I would let you do that instead of your Standard. It might be a minor rules break, but you're not technically trying to cheat, you're trying to do something small instead of something big.
No, RAW do not allow for any way to take more than one swift action per round, nor to use a standard, move-equivalent, or full-round action to do something that can normally be done as a swift action.
That said, as a DM I've always allowed players to sacrifice their standard action, but not their move action, for a second swift action, but only if they are significantly different types of swift actions - so using a skill trick and casting a swift spell would be ok, but not two swift spells, and probably not for a swift spell after having used Feather Fall as an immediate action.