What is the phraseology for an aircraft wishing to change frequency, but you do not want them to?

The correct phraseology for an aircraft wishing to change frequency, but you do not want them to, is "Remain on this frequency." This option is preferred because it clearly instructs the pilot to continue using the current frequency without ambiguity. The word "remain" conveys both an authoritative presence and clarity in communication, reinforcing the importance of staying on the same frequency for coordination and communication purposes.

While other choices may imply a similar instruction, they might not be as formal or precise. For example, "Please hold your frequency" could be interpreted as less direct and might not carry the same urgency. "Stay on this frequency" is somewhat informal and may not fit standard phraseology protocols. "Do not change frequencies yet" is direct but could come off as vague regarding how long the pilot needs to stay tuned to the current frequency. Thus, "Remain on this frequency" is the most effective and standardized instruction for maintaining communication integrity.