My question is motivated by a remark done by Tegmark in his book "Our Mathematical Universe". He says that GRT does not prove that relative speeds between material points are always smaller than c. It would prove it only for material points traveling through the same point. He needs it for the consistence of a supposition that in the frame-work of the expanding universe, galaxies from opposite sides can achieve relative speeds bigger than c one relatively to the other. So a first question is if GRT is really compatible with distant masses in relative movement with relative speed bigger than c.
My interest is not centered on cosmology, but in the logic study of formal theories. So I change a little bit the question, and I ask (as second question) if GRT is compatible with relative speeds bigger than c for pairs of inertial frames, which are necessarily distant. This question is important in the following context: if it is true, then GRT is not a conservative extension of SRT (in the sense that not all theorems proven by SRT are also true in GRT). [This would be because SRT sharply prohibits such a situation.] Examples of theories which do not exactly include other theories are well known. For example SRT is not a conservative extension of Galilean Relativity, despite the fact that both of them contain the principle of relativity.
However both questions are important and a positive answer to any of them can be interpreted as GRT not being conservative extension (from the logical point of view) of SRT.