Guess 2/3 of the average with integers - mixed strategy equilibria?
Quick note: in pure strategies for sufficiently many players, shouldn't all 1 be NE as well?

Onto mixed strategies:

To have a mixed strategy Nash equilibrium, each player needs to be indifferent between the strategies they are mixing and they must prefer all those strategies to the ones they never play.

That means players must mix only between strategies between which they have an equal probability of winning (when given all other players' strategies). I suspect you can use this to show that players must mix between 0 and 1. Then it remains to solve for whatever mixed strategies give which players indifference between 0 and 1.