It is possible but extremely difficult to knock off 3 heads in MK1. I can easily do the double one in Mk1 with no issue and I always try for a third and I always miss the third but Cage will crouch and attempt a third if you get the timing right. One time, only once did I get three heads in MK1. It more than likely was an accidental success but once I did get 3 heads.
Just as you would get 2 heads you just do the same for the third input but I do notice that the timing must be slightly faster for the third than the second head. Do Johnny Cage's Deadly Uppercut F, F, F, HP then count to 1 and do F, F, F, HP again to get the 1st and 2nd head (within 1 second Cage should have knocked the 1st head off which is when you should attempt for uppercut 2). To get the third head, or a third missed uppercut as soon as you input and get the 2nd head do F, F, F, HP again immediately. Cage might miss the third or he may get it so it may be up to the computer to give it to you?
Here is how I got it the third head. The input will include the 2nd head and go into the 3rd head: F, F, F, HP, count to 1 then F, F, F, HP, F, F, F, HP to get 3 heads. When you're trying for the 2nd keep hitting F, F, F, HP in case you get the 2nd, Cage should do the third uppercut/head decap that is how I got it.