FormerlyHemlock
Hero
I haven't fully read through the DMG yet so I'll take your word for it.
In game terms though, how would you rationalize a first level wizard that survives a tenth level encounter suddenly having the ability to cast spells several levels higher?
Er, to be fair, that's a general problem with the XP system. How would you rationalize a first level wizard that survives ten encounters with 8th level encounters over the course of six months suddenly having the ability to cast spells several levels higher? Once you figure out an answer to that question, you can answer the question of whether levelling up multiple times in a session is realistic.
In my games, you gain all the XP, but can only level up once per session. It takes you some time to fully process all your experiences. Players are okay with this.