Quasi System Administrator responsibility can't assign certain resonsibilities to users

We have created a responsibility that is similar to System Administrator but with a few exceptions. Using this responsibility, if someone tries to assign a certain set of responsibilities using Security>User>Define, they do not appear in the LOV and if you even try to type the first few characters you receive a message that it is invalid. These same responsibilities can be assigned using System Administrator. The responsibilities themselves were designed to be used to work with a different org, so they have some profile options to reflect that. I suspect it might have something to do with security grants,