The key to slam bidding is to be sure to have mechanisms to set the suit in all cases. Jumps in unbid suits are used to artificially set a suit and force to game. For example after:
3H sets hearts
4C sets clubs
3S sets diamonds (3D would be weak)
Suit setting bids are game forcing natural bids and jumps in suits that can't be natural at that stage. When there are multiple denominations that you might want to set artificially then the cheapest bid shows the one closer above (in a cycle), etc.
Making suit setting a priority means that 4NT is freed to be a natural bid in most auctions where a fit has not been readily found.