What must I do to get my single engine CFI rating?
Thanks. I see absolutely no reason why this should even be an issue. If you can instruct in multiengine, the single engine CFI endorsement should be a given as long as you have the single engine land on your license!
There are a number of maneuvers in the CFI-ASE check which aren't part of the CFI-AME program. The FAA wants to be sure you can teach, not just do things like chandelles and 180 power-off approaches. If you've reviewed that Additional Rating Task Table, you've seen how little there is to that ASE add-on, but they are the things nobody's ever checked you on teaching.
Prometheus At AOPA:
Ron is normally correct however we at AOPA don't see how you can add an additional instructor rating without additional endorsements. In particular, per 61.187(g) an endorsement for receiving and logging training per 61.187(b)(1), an endorsement certifying proficiency to pass a practical test on those areas in 61.187(b)(1), an endorsement that you received and logged training time within 2 calendar months preceding the month of application in preparation for the practical test per 61.39(i).
Upon further review of 61.183(g), I agree with Prometheus and have deleted that statement from my original post.