If a player has played "German Immigrants" to double subsequent PCFs in the Midwest (for example), can they then play a card for a campaign action on a later round + a personal appearance to quadruple their PCFs generated?
An -excellent- question. I am flattered that you're putting so much thought into the game!
The German Immigrants card reads,
"The Republicans double the number of PCFs played or generated in the Middle West for their Party this turn, regardless of the means by which they were acquired. Re-shuffle the deck when this turn completes."
As written, that means that a scenario as you describe is possible under the letter of the rules. However, do remember that the Republicans do not normally have a Personal Appearance in game. If they do earn one, and they then have this card available to play, it may well behoove them to do so. So yes, killer combo, but not likely, and not a game winner in and of itself.
The math might work out like this:
I play the German Immigrants card as the Republican. On my next move, I play a four PCF card to campaign in the Midwest, doubling my available PCFs to eight. However, I also decide to play a Personal Appearance, doubling that number again, to sixteen.