No, there is no such thing as a 'group right' Marxist, etc. Only a group of individuals, each with separate interests that may largely coincide.
And in the case of common resources, then, are we to say that everybody has individual rights?
That's what's led to so many of today's environmental problems.
Or what about eminent domain, in which the interests and rights of a group of people are determined to outweigh those of a single landowner?
Is every member of Congress allowed to impeach the President if he so desires, or mustn't Congress exercise that right as a group?