Stitching / merging multiple maps into a bigger map

I’m working in Java with libgdx.

I’ve made with Tiled some 9x9 maps that will be used as presets for a bigger map, 4x4 grid, i generate with an algorithm for a procedurally generated dungeon so i will end up with a 36x36 tiled map. The 4x4 grid will tell me the type of preset map to put. I’d like to merge/stitch those “presets” in this bigger map but i can’t figure out how to do this. Is it possible?

This is really a question about how to do this in libGDX, right? I would recommend asking in their community, if you haven’t done so already.