It is possible for a Drops campaign to be limited to a specific channel. An example of this is Rust, which at times runs a Drops campaign for all eligible channels, and then separate campaigns for a set of specific streamers that is only available on their channels, and offers a reward related to their channel.
There’s nothing to stop someone opening multiple streams and being counted in multiple campaigns at the same time though.
One option could be to have users select a streamer to support on your website, lock in that choice at some point so it’s not changed just before the outcome decided, and then when the user claims the drop you could fulfil the redemption differently on your side based on the users selection.