A twin-engine F-35 would be a new aircraft

Could a larger twin-engine F-35 retain the existing aircraft's capabilities?

Doing so would require enough redesign to justify a new aircraft type, even if procurement politics encouraged keeping a familiar designation.

Turning the F-35 into a twin-engine aircraft while retaining its capabilities would require extensive engineering changes. A new designation would normally follow because the result would be a different type. A familiar number could nevertheless be retained to make congressional funding easier to obtain. The Super Hornet supplies the comparison: family resemblance and an upgrade label can conceal a substantially new aircraft.