I am not an expert in this field but the idea is basically to get your immune system to recognise the enemy. For example, IIRC the vaccine for small pox was a dose of cow pox, which is similar but not harmful to humans. Your immune system spots it, destroys it and then when the real thing comes along, it gets destroyed as well.
Watching the news it looks like all the vaccines are using the same approach for enemy recognition i.e. the same characteristic of the virus.
This would suggest that taking all the different vaccines would not boost your immunity but I could be wrong.