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(highlights 'could' in thread title)
By this I guess I am assuming if he used all usable resources perfectly, had extremely competent generals, no revolts, and just generally good luck.
Personally I think he would not have gotten too much more. The Frankish "infestation" of Gaul was too cemented by then. It would have been a long slog through the countryside, and Justinian does not have the time, money, or supply lines for that IMO.
Perhaps more of Hispania and rest of African coast?