Nope, you can't just move posts around in your basement at will.
You could have a joint in that beam that can't easily be seen with the post there,
you will need poured concrete support footers under the new posts,
and you need to take into consideration what exactly is above the posts and the beam.
Best left to a professional at least to evaluate your situation. We can't see what you have from here, so it would be best to get someone to look at it before you do anything.
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