There is no rule barring an overlapping territory. What matters is whether the enterprise is real and operating or credibly ready to launch, whether the capital is substantial and genuinely at risk, and whether projections built on the remaining customers still support non-marginality. Resolve the granted rights first.
Decide what the overlap costs the plan
Ask the franchisor, in writing, which addresses, accounts and referral channels the existing operator keeps. Then price the difference: fewer reachable customers may mean a smaller build, different staffing, or a second site. If the revised plan can no longer support more than a minimal living for the household, discuss whether a significant economic contribution is demonstrable, or whether the territory itself should change before capital becomes irrevocable.
Put a date on each unresolved fact rather than leaving it open. Ask the franchisor for a written answer by a stated day, ask counsel for the conflicting-obligation review by another, and fix the day on which, absent an answer, the plan moves to a different territory. Deadlines you set yourself are the only ones here you control.
One condition does not soften while an overlap is negotiated: the investor must develop and direct the enterprise, so an arrangement in which the franchisor or a manager makes the operating decisions through a long stand-off weakens the very case the delay was meant to protect.