Fr8dog,
Let's look at the requirements for the high altitude endorsement, as well as your privileges as a flight instructor. First, you ask if you can provide instruction in a multi engine airplane, when you don't hold multi engine privileges on your flight instructor certificate. The answer is no, you may not.
Refer to 14 CFR 61.195(b) & (f). In order to provide flight training, you must hold appropriate category and class ratings on your pilot certificate (commercial multi engine airplane land, in this case), as well as on your flight instructor certificate (Flight Instructor, Multi Engine Airplane). Additionally, you must have five hours as pilot-in-command in each multi engine airplane in which you provide flight instruction or flight training.
Next, let's address the issue of being rated in the airplane. Are you rated? Yes, you hold a multi engine land rating on your commercial pilot certificate. Category and class. Is your student rated? Yes: he holds a multi engine land airplane rating on his airline transport pilot certificate. An endorsement is not a rating. He is rated in the airplane, but may not act as pilot in command of that airplane until receiving the appropriate endorsement.
The high altitude endorsement is not type-specific. Your student may receive his training in a flight training device or simulator to meet the requirements of 61.31(g), or a single engine airplane. However, the training must include normal cruise flight operations while operating above 25,000 MSL.
You can provide the necessary flight training if you wish, but not in a multi engine airplane (which rules out the king air). You may also do it in a flight training device or simulator which is representative of a pressurized airplane. You may also do it in a single engine airplane, remembering that if you do it in the airplane, the language of the subparagraph 61.31(g)(2)(i) requires it to be done above 25,000' MSL.
The flight training requirement of 61.31(g)(2) was established upon recommendation by the NTSB, following a series of accidents in the 1980's.