Grow the other species in bags first. Once you have harvested the bags, soak them in compost tea then break them into spawn chunks and bury them mixed in wood shavings (not Cedar or Juniper shavings).
Oyster is very aggressive, it will even stun and digest nematode worms. Your other species needs a healthy running start if you already have established oyster mycelium.
Use the same media in your bag as you are going to be spawning to outside. Mushrooms can turn on/off dna code to grow better in their environment. if you spawn to the same substrate, it will already know what to do.
Feed your oyster colony wood chips, coffee grounds, and dead leaves.