The Constitution states the only possible restrictions on presidential power, thus a president can exercise the powers of the office except if dies, is impeached, or the 25th Amendment becomes relevant. If the VP decides to can can get a majority of the relevant principal officers to agree, POTUS can be deemed unable to discharge his duties. Congress has not designated any body other than the executive departments for satisfying that requirement.
After the disability is communicated to the President Pro Tempore of the Senate and the Speaker of the
House, the Vice President immediately assumes the powers of the president. However, the declaration of disability is revoked when the president informs the Senate Pro Tempore of the Senate and the Speaker of the House in writing that no inability exists, and he resumes his powers. Then, if within 4 days the VP and a majority of the cabinet again vote that the President is incapacitated and communicate that decision as above, then POTUS does not resume his powers.
If and when this comes up, there will be some discussion about the timing of the re-vote. The amendment says, specifically
Thereafter, when the President transmits to the President pro tempore
of the Senate and the Speaker of the House of Representatives his
written declaration that no inability exists, he shall resume the
powers and duties of his office unless the Vice President and a
majority of either the principal officers of the executive department
or of such other body as Congress may by law provide, transmit within
four days to the President pro tempore of the Senate and the Speaker
of the House of Representatives their written declaration that the
President is unable to discharge the powers and duties of his office.
Assuming that the inability is not instantly re-certified, then there are at least two ways to interpret this. One is that the president temporarily re-assumes power until 4 days pass or the disability is re-affirmed. The other is that the president must wait 4 days before re-assuming power (and the VP remains in power). Then SCOTUS will have to decide what the amendment "means".
Assuming that the inability is re-certified within 4 days, then by a vote of 2/3 of both houses of Congress, Congress decides if POTUS is disabled. Specifically:
If the Congress, within twenty-one days after receipt of the latter
written declaration, or, if Congress is not in session, within
twenty-one days after Congress is required to assemble, determines by
two-thirds vote of both Houses that the President is unable to
discharge the powers and duties of his office, the Vice President
shall continue to discharge the same as Acting President; otherwise,
the President shall resume the powers and duties of his office.
In this case, the language of the amendment makes it clear that the VP becomes acting president. The unclarity is limited to whether, between declarations of disability, actions of POTUS are legal.