The Supreme Court just effectively eliminated recess appointments. If the filibuster ever gets restored to the level Republicans want it to be, it would give a Senate minority the power to shutdown the executive branch, and do great damage to the judicial branch.
There needs to be a constitutional amendment for appointments. It might read something like this:
If the President makes an appointment that requires Senate confrirmation, the Senate has a 3 month period to approve the appointment by a simple majority vote. If the Senate does not vote on the appointment within 3 months, the appointment is considered confirmed. If an appointment is made while the Senate is not in session, the appointee can take office until the Senate goes into session and votes on confirmation, with the 3 month window starting when the Senate goes into session.
Note the specific requirement for a simple majority.
I also think the number of offices that require Senate confirmation should be reduced to a couple of hundred in the Executive branch. But I don't think a Constitutional amendment should be used for that purpose.