If the game published in 1 Button Jam updated and add another button to it, could I use it to join this jam? Or only new game allows to join?

Well, it's not the most interesting take on the jam, especially when you managed to make a 1-button game, which is harder. I'd rather see updates and enhancements to 1 button games than see them transformed in 2 button games if possible :D

But if you feel your game didn't feel right with 1 button and that it would be better with 2 buttons, you can go for it! I guess you'd have to submit and second game though, or remove it from the 1 button entries maybe?

I think I might keep update the 1-Button version while making 2 for the game for 2-Button version if I got enough time. I'll figure it out. 

Thanks you, Feldo.