You are right that it is thought we will collide with the Andromeda galaxy, but it will not necessarily mean more supernovae, which are deaths of old stars, in fact it will probably cause more star births.
If you imagine the Sun as a grain of sand, on the same scale the nearest star, Proxima Centauri, would be about 15 kilometres away. That is the amount of 'empty' space in the galaxy. So the stars themselves will be unlikely to hit each other.
Not quite empty because there is a lot of gas and dust which we see as the great range of nebulae, and when galaxies collide this gets compacted resulting in the creation of more stars.
On the other hand, we think most if not all galaxies have at their centre a "supermassive black hole", and depending on which side of our galaxy we happen to be on at the time of the collision, our solar system might or might not get swallowed by it.
But this will not happen for about 5 billion more years, if we don't miss altogether.