No; buildings are not currently moddable, and grates are buildings.
You'll have to have at least 3 floors per 4x4 area to fill the other 13 squares with grates, or more for a bigger space. Unless... Hmm...
I don't know for certain if this will work, but there is a bug involving constructed walls that you might be able to use. If you build a constructed wall, the top of that wall is treated as a floor for all other purposes, including building buildings on top of them. However, once the building on top of the wall is built, you can remove the wall and the pseudo-floor that once supported the building above goes away as well, leaving the building hanging in midair, even if it would normally require a floor underneath it. You can get non-anchored drawbridges, floating floodgates, and the like with this technique.
So, what I'm thinking is this. On the level below where you want your grate square, build a number of walls, like so for a 4x4 square:
++++
+O++
++O+
++++
Then, on the next level up, build all 16 grates; the floors from the walls below will support the 4 central grates. Then, remove the walls. If all goes well, you'll then have a 4x4 square of grates, easy and done with forever. If all goes badly, the 4 central ones, being unsupported, will promptly collapse, crush-kill-destroying at least one of the people removing the walls. Or, the central 4 might simply deconstruct harmlessly. Regardless, for safety's sake I'd recommend turning off caveins before you attempt this exploitish workaround.