How do you say when you’re holding the door for someone for example and you’re trying to say the equivalent of “I insist!” when they hesitate to go ahead? Can you just say “S’il vous plait!”?
Informally, you can simply say:
Vas-y (if you are on a "tu" basis with this person)
Je vous en prie / je t'en prie
More formal, if the person wants you to go first and you want to insist:
Je n'en ferai rien
(Note: I have some doubts about using s'il vous plait in such a situation. I come from a region (Belgium) where we use it a lot more than in standard French, and yet I would personally find it a bit awkward in that particular situation. Some may disagree.)
You could simply go with
Je vous en prie / Je t'en prie
Which is quite formal and unisex. Keep the second one for people you say "tu" (=tutoyer) but still want to keep some kind of formality. I could use it with my boss for example, which I call by his firstname and say "tu", but still keep some kind of distance/respect :-)
Other formulas :
Après vous/toi ! (neutral, meaning "Je passerai après vous")
Honneur aux dames ! (To use only with women, or with male friends if you wanna tease them a bit :-)
Honneur aux anciens ! (To use with elders, with caution. I use it almost exclusively to tease people a bit, like a joke on how old they are. Most people you don't know that well could be offended though as you're basically implying they're old.