What are you setting this on? If you’re building this from the floor or sub-floor up, then all your pieces simply get screwed down to the floor/joists. Construction adhesive between the layers would be fine, but maybe not necessary. I’m not familiar with “fiberrock” (as you described it), but have built a number of tiled floors, showers, & countertops. Most often I’ve used Durock (comes either 1/4” or 1/2” thick) for the tile base, and that means mixing up and spreading a thin layer of thinset to lay the Durock on (after the substrate plywood, or whatever, is securely in place), screwing the Durock down to the substrate with special screws, then fiberglass tape and more thinset to seal the joints between the panels of Durock, then thinset and the final tile, then grout and finish. Since you screw down the individual pieces of plywood, then thinset and screw down the Durock, then seal the joints, there’s no need to fasten them to one another along any of the edges...unless you think you’re building something that could be moved one day, but that’s not what it sounds like to me, nor is it what I’m trying to describe (nor is it anything I’d ever want to try to move). That would be an entirely different story. Since you’re just looking to build something structurally sound and not waterproof, you could probably do all this even more simply. Rick