How many times can a single character start a New Game Plus?

• NG+1 starts at level 51.
• NG+2 starts at level 81.
• NG+3 starts at level 100.
• NG+4 starts at level 120.
• NG+5 starts at level 120 too.

So yeah, it appears there's no end to how many times you can NG+ — but there's also no point.

These numbers are fixed. If your character has a higher level than 51 at the start of NG+ (my Engineer was level 54 when he made the jump), the game will still start at level 51 and monsters will adjust in their allotted level brackets accordingly.

Before you start planning your wonderful adventure towards and beyond NG+∞, you want to keep in mind that your character can only play in multiplayer with other players in the same New Game Plus tier. That means you will need to start a new character at level 1 to play with friends who are still midway their first quest.

New Game plusses can continue indefinitely. They start becoming extremely challenging at New Game+++, where mobs start at level 120 (versus your level cap of 100).

(Source)