As long as the smaller claim is valid and up to date there should be no problems. If the big boys want it, they either have to lease the rights from you or buy the claim from you. This is of course provided that they want to play fair.
Um? the answer is they can't? If you have a valid claim that's why claims exist.
The big companies our not our enimies and they are not out to steal youir ground.
In fact many of the big guys rely on small scale prospectors to find them ground. Exploration is expensive for big companies and a lifestyle for small guys. It's a perfect relationship.