Adding Poured Foundation under existing Porch

I have an porch which is supported with laley columns. It is not very old and it is in excellent shape. I want to make it into a heated room. Is there a way to put a standard poured foundation under it and somehow connect the botom of the sills to the wall? The columns are solid, there are no saging or springy floors. I just feel that a foundation is better.
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Sure... this is an easy one.
Tear out the porch and pour a foundation. Then, build the walls and add the heating.
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