You mean blend modes, not layer styles. There’s the hard way, and the easy way – I only know the hard way.
Here’s what you do.
You have a base layer. You add an adjustment layer or put another layer on top of it – let’s just say "adjustment layer" for the sake of clarity, but realize it can be any layer on top of the base.
Change the blend mode to Multiply. There are a couple of ways to do the next step, here’s an easy one. Edit|Copy Merged; Paste. You have copied everything that’s visible into the clipboard and pasted it as a new layer – a "composite" if you will.
Add your next layer, or copy the previous one you used (your call) and put that above the "composite", change blend mode to Darken.
Repeat as necessary.
Peace,
Tony