Installing Slate floor tiles over a plywood floor

You can lay on top of plywood as long as it is WBP (water boil proof) Marine Plywood, this has been treated & is much stronger than standard plywood.

It is also recommended that a minimum of 15mm marine plywood is used & that the floor does not flex.

If it does then a more solid method would be to cross lay 9mm WBP Marine Plywood on a horizontal direction screwed down at every 300mm intervals & then overlay a second layer of 9mm WBP Marine Plywood on a vertical direction screwed down again at 300mm intervals.

Remember to use a bonding agent to prime the plywood & a flexible grout & adhesive.