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... ne cuius suorum popularium mutatum secum fortunam esse uellent....

This should be "mutatam" in agreement with "fortunam," that is, the "fortune/lot" of "anyone" ("cuius" = "alicuius" after "ne') of "their own countrymen/peoples" be exchanged ("mutatam...esse") with themselves ("secum"). Note the use of the reflexive "se" referring to the subject of the subordinate clause. "