upanisad phase of india led to further ramificaions of thoughts resulting in various permutations and combinations of philosophies.
notable among them were the sankhya,yoga ,nyaya ,vaisoshika,and mimasa.of these mimasa is closest to traditional upanisad thought. yoga and sankhya appear to have lesser influence of upanisads and some even propose they were pre-upanisads.
needless to say sarvaka, jainism and buddhism phase followed in early maurya periods.there was revival of hinduism in guptha periods and all over india several new systems developed with varying influence of upanisads.
saivasiddhantham is one among them-with the distinction of being a siddhantha school, a form some what distant to the vedantha spectrum.
in the 8th century onwards individual philosophers became prominent and their schools like advaitha,dvaitha, visishtadvaitha ...etc was popular with certain circles.
during the muslim rule of india the upanisads were translated to turkish,persian and arabic. there was even an effort by Akbar to write an allaho-panisad. aurangazeb's brother was a vedic scholar.
during the european phase royal asiatic society at calcutta translated upanisads and was popular among europeans. it is was influential among the existential circles.
movements like aryasamj and brahma samaj took inspirations from upanisads. in 20th century tagore, mahatma gandhi were the modern face upanisads to the world.