The downstairs bath ceiling started showing water damage. We took part of the ceiling and wall behind the toilet out, to look at the pipes/tub from below. Up stairs, in the tub, the faucet area has a hole in the stainless steel soap dish, which is all one piece. The faucet/handle/soap dish. Whem pouring water down that holw, it leaked right down to the bath downstairs. So, for a temp fix, until we had the money to get the supplies, we used a soap dish and a heavy duty glue to attach it over the hole. It worked for about a week, then it started leaking again. We have a new faucet/handle/shower head we are going to install, we are also going to take the tile out and replace it with a surround.
What I'm asking is, could the leak be coming from somewhere else, say, the shower head area? I suppose we will know when we rip the whole wall out.

Yes, it could be leaking from just about any pipe and any connection in the plumbing. Also, it could leak from any screw in the wall (shower door, enclosure), soap dish, niche and / or missing grout. It could leak from shower pan, drain, and/or trap.