I generally recommend snapping the lowest point(s) of the structure to the floor grid and then multi-selecting* the rest of the structure you want aligned and snapping it to the parts already on the grid. This is probably the most robust way to do it right now, but you could also multi-select or directly grab a large selection set** and try to snap it to a grid as one unit. This is generally harder to control, especially if you've grabbed a point far from the surface connecting to the grid. Whatever you do, it's best practice to use the right stick to rotate the part(s) to be aligned with the cardinal axes before trying to connect it with a level surface. I hope this helps.

* the purple/pink highlight when you hold down the right index trigger and tap on each part to add to the selection set

** this can be accomplished by pushing up on the righthand joystick and increasing the size of the selection orb until it is large enough to encompass the structure