It depends.
First, was the existing structure (Columns and footings)designed to accommodate the additional loads for a mezzanine?
If so you need to find out what loads it was designed for. If not, you need to design an independent structure. Two things will govern. The anticipated or required design loads and the spacing of columns. The greater the loads and the larger the column spacing the deeper the members will need to be, or the stronger the material or both. Shorter spans can use dimensional lumber. Longer spans need engineered lumber. Even longer spans need steel.
So first find out what code requires for loads, or what you will actually load it with if more than code. Decide on the layout and column spacing. Then it can be engineered.
Do you want it mostly clear of columns, say 1 column? Or can there be a partial load bearing wall under it?