You can use movement of nouns and possessives to eliminate all but one of the occurrences of 'of the' from this: "among the rights of the undergrads of the University of the Basque Country")...

Among The University of the Basque Country students' rights

I am supposing the following: the proper full name, in English, of the university is exactly this: "The University of the Basque Country" I do not know enough Basque to tell if Euskal Herriko Unibertsitatea would need a definite article, but it seems to me that Universidad del País Vasco does not have one. In any case, English educational institutions are often referred to without any article:

Among Oxford University students' rights

If I am correct in this, then the following natural, and not at all awkward construction is possible:

Among University of the Basque Country students' rights

You can use movement of nouns and possessives to eliminate all but one of the occurrences of 'of the' from this: "among the rights of the undergrads of the University of the Basque Country")...

Among The University of the Basque Country undergraduates' rights

('Undergrads' is informal)

I am supposing the following: the proper full name, in English, of the university is exactly this: "The University of the Basque Country" I do not know enough Basque to tell if Euskal Herriko Unibertsitatea would need a definite article, but it seems to me that Universidad del País Vasco does not have one. In any case, English educational institutions are often referred to without any article:

Among Oxford University undergraduates' rights

If I am correct in this, then the following natural, and not at all awkward construction is possible:

Among University of the Basque Country undergraduates' rights

You can use movement of nouns and possessives to eliminate all but one of the occurrences of 'of the' from this: "among the rights of the undergrads of the University of the Basque Country")...

Among the University of the Basque Country students' rights

You can use movement of nouns and possessives to eliminate all but one of the occurrences of 'of the' from this: "among the rights of the undergrads of the University of the Basque Country")...

Among The University of the Basque Country students' rights

I am supposing the following: the proper full name, in English, of the university is exactly this: "The University of the Basque Country" I do not know enough Basque to tell if Euskal Herriko Unibertsitatea would need a definite article, but it seems to me that Universidad del País Vasco does not have one. In any case, English educational institutions are often referred to without any article:

Among Oxford University students' rights

If I am correct in this, then the following natural, and not at all awkward construction is possible:

Among University of the Basque Country students' rights