Yes. It is entirely biblical. It's not taught so much these days, which is a great shame. The whole "once saved, always saved" v "Christians can lose their salvation" debate would be over if people understood the principle of two salvations.
The problem with Christian jargon is that the meaning can become restrictive or turned into a code. "Salvation" has become pretty much going to heaven when you die. It is vastly more than that. If people substituted the word "deliverance", which is just as correct, the meaning may become clearer.
The first salvation is when the individual is born again. It is instant and entirely God's work. The salvation (deliverance) of the soul is God's work but requires our cooperation. So an individual may be born again but show little or no sign of it because they have not allowed God to work in their lives.
To be effective in God's kingdom we must be set free from the old habits and memories of our pre-Christian life. We bring our old attitudes, thought patterns, selfish desires, misconceptions etc with us. Some are changed very quickly, others take a lifetime. The spirit is where we gain spiritual knowledge. The soul is where that knowledge is expressed. A dysfunctional soul hinders our walk. God delights in setting us free, but it is only with the cooperation of our will.
It's a massive subject, so what I've said is not even an introduction. If Christians ever let this truth get hold of them, their lives will be much different.