You might be able to achieve your goal of "uninterrupted" or "private" to some degree by using a digital protocol such as DMR. As such, you could form your own "Talk Group (TG)" and call specific stations to participate in the TG. Only stations with the correct settings (Color Code, Time Slot number and Talk Group number) could easily participate. You would be sharing the frequency with others in one of two time slots.
Note that other stations casting a wide net (so to speak) could still find and participate in the conversation if they bothered to do so. But, they would need to do so more deliberately and generally that doesn't happen. So, still wouldn't be private (in the encrypted or detectable sense), but total privacy and exclusivity is not permitted (in the USA at least).
