Ratings

I started a game with a player of similar ranking, but in the course of the game, their ranking soared over 300. How does this happen. They were clearly much higher than me

Clearly your opponent does not believe in chess monogamy. He or she is a 'chess slut', willing to play with anyone at anytime. All behind your back.

lol... did u come up with that yourself?

I realise players are playing more than one game, but how is a jump of 300 in the space of 30 minutes possible?

A possibility -- new ratings can rise or drop by large amounts in the first few games under the Glicko rating system (what chess.com uses). 2 or 3 wins against higher-rated players could produce +300. What was his rating when you began your game with him?

1100