For menu you can have different buttons. The 1-button rule only applies to actual gameplay, though it would definitely be an interesting challenge to figure out how to handle menus with the same button :)
As for having a second clickable button, that does count as a second button so it's not quite fitting for the jam. Think of a different way to change the action. Maybe holding the button changes the action? Or double/triple tapping it? Or maybe the action changes contextually. To give you an example, in my game if the character is on the ground the button acts as a jump button, but if the character is in the air it's a fire button.