I have heard that I can be a CFII without getting my CFI. Is this possible?
Yes you can be a CFII without getting your CFI. In other words, you can be a certified flight instructor with an instrument airplane rating and not airplane single and/or multi-engine rating.
Remember, Certified (certificated) flight instructor or CFI is a certificate, with the following possible Ratings:
Airplane single engine and/or multi-engine
Your Flight Instructor certificate, if taken as a CFII as initial issue, will indicate as:
You will be limited to teaching only Instrument maneuvers, and instrument rating students. As the flight instructor rating is Instrument Airplane, so you are allowed to teach either in a single or a multi-engine airplane, but that is a whole separate discussion, and we will do so in a different post.
To obtain your CFII as an initial CFI certificate/rating, you will need to accomplish everything required for the CFII rating plus FOI. The FOI knowledge exam has to be passed, and during the checkride you will need to meet the FOI knowledge requirements just the same as a normal CFI initial applicant.
How about if I want to add airplane single and/or multi-engine rating later
Sure you can do so. Just skip the FOI portion and be prepared with the rest of the CFI airplane SE or ME PTS.