Does the Yoga system, unlike the Sankhya, admit to only one purusa?
In SAmkhya there are infinite Purushas. And, the Prakriti or Avyakta's only task is to selflessly work for their Bhoga and Moksha.
In Yoga too it's the same it seems. And, it is also a fact, that on many points Yoga is based on SAmkhya. SwAmi VivekAnanda mentions this many times in his commentary of the PAtanjala Yoga Sutras.
Only difference between the two is that, in SAmkhya there is no acceptance of a God or Iswara, which on the other hand, is clearly accepted in the Yoga Darshana.
See, the following relevant verse from the PAtanjali Sutras SAdhana PAda:
KritArtham prati nashtamapyanashtam tadnyAsAdhArantvAth || (22)
Translation (as per SwAmi VivekAnanda; i have translated into English upon seeing his Bengali translation):
Although, for one who has attained that Absolute, the Prakriti (or AgyAna or false knowledge) ceases to exist, but for others it still is very much working.
The Atma or the Purusha is completely separate from the Prakriti- to make Purusha realize this- is the sole task that the Prakriti has. And when the Atma realizes this for a fact, then the Prakriti can not attract him towards it any longer. One who has been liberated, for him, the Prakriti is completely dissolved or non existent. But there will be always infinite number of such Atmas or Purushas for whom the Prakriti will always continue to act.
So, this is quite clearly talking about infinite Purushas, like they do in SAmkhya.
JanmamaranakaranAnAm pratiniyamAdyugapat pravitteshcha |
Purushavahutam siddham traigunyaviparjayAcchaiva ||
Due to the difference of rules (Pratiniyama) regarding life, death and the Indriyas (Karana), due to the fact that none of these occur simultaneously [for anyone] and due to the fact that differences among the three states (Traigunya viparjaya) are everywhere seen, the multitude of the Purushas is thus been established (Purusha vahutam siddham).
SAmkhya KArikA verse 18.