It is generally ok for a cave instructor to take someone one level up from their current certification.
It is not ok for a non-instructor to do so.
Example: I am a cave instructor. You are a cavern diver. Probably ok to take you on an intro-to-cave level dive provided you have the right gear, technique, etc.
Example: I am a full cave diver. You are a cavern diver. I should not take you on an intro-to-cave level dive, regardless of you gear or technique.
Rationale: cave instructors by their very nature are taking divers up to the next level. They have specific training and experience to do so. Non-instructors do not formally have this training and experience, nor the insurance for it.