Mountain formation isn't the best known process in the world. The general process for the formation of the Himalayas is described in Wikipedia, as isare the various disagreements on the pre-Himalayan geology.
The general subject for disagreement is which parts of the Indian and Eurasian plates along with the Tethys seabed ended up where. Le Fort, 1975 extensively documents the known (in 1975) ages of deposits in various parts of the Himalaya. The general facts are, and this is well illustrated by Fig. 2 from the paper on page 4, that there are some regions of the Himalaya where surface deposits are Triassic in origin (200-250 mya), while other areas such as Kumaun district of Uttarakhand state have deep Eocene marine sediments as young as 40 mya.
After this collision, there was still the Tethys sea between India and Eurasia, and itEurasia; the Lhasa terrane was separated from India by oceanic crust. It took tens of millions of years to close thatwhat was left of the Tethys sea. The rest of the continent of India didn't start to collide with Eurasia until about 55 mya. This collision re-ignited the Gangdese volcanic belt and causing the Jinsha suture to rise from from 50-20 mya. This phase of the collision probably coincided with volcanic mountain building of the same sort that made the Andes and Cascades in the Americas. A detailed (and very readable for a paper, in my opinion) description of this phase is in Jain, 2014.
Over at Earth Science SE, there are a few posts talking about maximum possible heights of mountain ranges. Without going too much into detail, the Himalayas are probably about as tall as mountains can possibly get; since at about 8000-9000m, erosion rate from glaciation starts to exceed maximum possible uplift. So the conclusion from Sorkhabi and Stump is that for those three pulses, including the one at present, the Himalayas were about as tall as they are now.
An analogy to the situation in today's world would be this. The Persian Gulf and Mesopotamia is a foreland basin between the Iranian Plateau in front of it, and Arabia behind. The gulfGulf could (if the plates were lined up just right) rise into Himalaya-sized mountains in 4 million years. However, there would already have been a significant mountain range in the area before this 4 million year orogeny started; they just wouldn't seem so significant once there were 8000m peaks towering over their southern border.