In classical Greek philosophy, the non-material "soul" was much more than 'just' a spirit. It was an eternal essence that pre-existed the birth of an individual and post-existed (survived) the body's death. The 'soul' was the perfected rendition of the material body that was seen to be imperfect (and subject to sickness, death and decay). Upon death, the soul was released from its cloak. In this, the immortal soul was seen as 'higher' than the mortal body. So I think that one cannot merely transpose one concept into the other. There is much to differentiate classical Greek ideas of the soul and what has come into Christian faith.
One also has to understand the Hebrew concept of life and death, because it is relevant to the bible, as a Hebrew creation. In Hebrew thought, the body/soul was one entity and indivisible. At death, the 'person' is placed into the ground, into Hades, but is fully conscious. There is no separation of body/soul as for the Greeks. This understanding enabled a belief in apocalyptic resurrection. It provided the framework for it to be expressed.
Probably, one reason why the Greek concept of soul came into Christian faith, was the Apostle Paul's use of the Greek philosophical framework to interpret Christian faith for his Greek-speaking audiences. There is a fine line between teaching a concept and re-interpreting a concept to help hearers/readers to understand it. Was St. Paul teaching the Greek version of soul or was he interpreting the Gospel in categories his Greek audience could understand? That's a difficult question to answer.
I think that modern science will also keep body and soul together as a single entity. When the brain function ceases then the person is functionally 'dead'.
But then there is the matter of resurrection. If time-space is an Earth-bound concept then anything outside of that, another planet, universe, or even another time-space dimension, is not subject to the same rate of time. Our "day" on Earth is a single revolution around the polar axis of the planet. ie one single spin of the planet from point to point. If we travelled to Mars a "day" would be completely different, as would a year, which is a single revolution around our Sun-star. So perhaps the point of death/resurrection is instantaneous by a different "time" rate than for usso that the two become an almost instant event back-to-back rather than two separate events separated by a long time. Just a thought.
At any rate, Christian theology has lived with the idea of "a bodily resurrection, a re-creation, a new heaven and Earth" and a cosmological reconcilliation (Romans 8; Colossians; The Revelation).
St. Paul does however, not discount the body completely. In Romans 12 and in 1 Cor. 6: 19f he points out the value of the body. This is completely at odds with the Greek conception that dismissed the body as having no eternal value whatsoever.
For Greek philosophy, the soul is eternal. The soul is split into two parts prior to birthing, representing its male/female components. So when people speak of "finding one's soul-mate" this is what it refers to: the re-joining of the male/female soul in eternity.
The question revolves around whether human beings have an essence. For the bible, the answer must be yes and no. Th Judeo part of Scripture won't be compatible with the Greek conception of soul. Paul's re-interpretation less so, but needs careful reading so as not to read foreign or assumptive elements into it. It's not clear that Jesus viewed humankind in a dualistic way - but then again, he was Jewish!