When you cannot put your own established patients into your schedule within a comfortable manner for both you and the patient then you definitely have too many patients and should not take any new ones.
Even if your patients love you expect some of them to stop seeing you cause their insurance changed, they moved, died, got better to the point where they needed to see you far less or not at all, or their PCP was able to continue their meds once you got them on the magic regimen. So you're likely always going to take some new patients here and there. You will have to, from time to time, close the valve and not take anymore.
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In your specific situation I wouldn't take new patients unless I had more knowledge of the hours of the psychiatrist taking over. Explain to patients you're transferring care. Make sure you follow federal and state laws with patients still having access to their records. You can write a termination letter to be safe but also stating you're referring to the new doctor to take over to CYA.