I think it could be done as you describe, by placing a plywood base that fits the tank footprint. The details of that statement are critical, however. For instance I would make the auxiliary base out of two sheets of 3/4" plywood, glued and screwed together. That would make your base 1-1/2" thick, with an overhang of the same amount. I would also fasten the new base to the stand with screws and adhesive. I would probably trim the raw edges with solid wood, that also would add strength. I think that the small cantilever would be well tolerated and the rim of the tank would be fully, and properly supported.
That is what I would do, if I was motivated to go to the trouble. Your results may be different than I suggest, but I would have no problem for myself. I have plenty of woodworking tools and experience, so that's what I'd do for myself.
If you have any misgivings, just buy a proper, commercial stand.