Hari Om
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As I look to this section of posts and information it would seem to me we would have all the 6 systems. As I have been taught, these systems do not compete but complement each other. It may be noted that each system is so complete in itself to give kaivalya to the practitioner, that some scholars may debate that one is superior then the other. This only limits ones vision of the vastness of this thinking and the richness offered to the family of man.

Nyaya- the science of reasoning
Vaisheshika - special qualities (vishesha) which distinguish one object from another i.e. vayu, apas, tejas, prithivi, akasha ( my favorite), kala or time, Dik or direction, atma, manas.
Samkaya - or pertaining to number. Most notable is Purusha and Prakriti, yet there are 25 components if I am correct which include the 5 mahabhutas ( akasa, vayu, tejas,apas, prithivi).
Yoga - We have posts on this and is directed also to Patanjali - the goal is union and the direct perception of Satyam and Dharmamega ( cloud pouring virtue), let alone Ritam. We are all aware of the siddhis, Yama and Niyama, etc. the 8 limbs that are pointed out in this practice.
Karma Mimansa or investigation, close consideration of action and dharma.
Vedanta or the end of , or final knowledge of the Ved. This explains/explores the relationship of the Absolute , this fullness ( Bhuma) or Brahman.

If there are those on this forum that can advance ones thinking here, it would be great. My attention has been more on the yoga of Pantanjali, the Upanishads & Jyotish. I would desire to understand more of Samkaya and the other systems.
Of all, I have tried to read the Mimansa Sutras but to no avail. A teacher is needed
for most on this subject matter.

I am happy to be viewed as a sisya for all these systems ... and perhaps the opportunity to know more.