John of Gaunt has no Male heirs

What if John of Gaunt has no male heirs and his only senior heir is the Avis Family could Gascony, Portugal and Britain be on personal union?
 
No. There's his younger Brother, Edmund, Duke of York and his two sons Edward and Richard. Edward was married already, but would die without issue. His brother would OTL, and seems very likely to have under the circumstances, marry Anne Mortimer who was descended from Edward III's 2nd son Lionel Duke of Clarence's Duaghter Phillippa.
 
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