Just like a plane without rockets? No. The higher you go, the thinner the air. A plane needs air to generate lift, which is what keeps the plane up. Once you get to a certain point, no plane can go higher, no matter how well-designed and efficient the wings, because the wings can no longer generate enough lift to go any higher. In theory, you could have rockets attached to the plane (or part of the plane) to get even higher, but I don’t know enough about orbital mechanics to tell you if such a plane could carry enough fuel to reach a semi-stable orbit (even at ISS heights there is still enough atmospheric drag to require an occasional boost to keep it there)
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