If they can be stacked, then I quit Pokemon forever.
Go <any typed pokemon>! *Dies instantly* I choose you, <next pokemon>! *Dies instantly* Okay, it's your turn now <next in line>! *Dies instantly* We can still turn this around... go <hahahaha>! *Dies instantly* **** you! *Pulls gun on other trainer*
Where did you come from? Where do you go? Where did you come from, demon-eyed Jho?
If they can be stacked.... the game just got broke.
So, assuming they cannot and they are mutually exclusive... this would be fantastic. Hazards are a huge part of competitive Pokemon. I personally think they are a great addition and add a level of strategy to the game. The problem with Stealth Rock is that there is only the one and that is is typed damage. Either by itself is not bad, but when those two qualities are together, it causes some Pokemon to be hurt significantly more than others.
With many types of mutually exclusive hazards, each team can choose the type that helps them most. Rather than sun teams using a move that cripples opposing fire types that they don't mind so much, they can run a Grass Hazard to damage Rain and Sand starters. Every team would pick the hazard that helps them most, and individual Pokemon who are currently killed by SR would get new life as the fraction of teams using the moves that cripples them specifically would drop dramatically. Overall the hazards culture would still exist, but no individual would be ridiculously hampered by it in the metagame as a whole.