I'm not sure I fully understand the question. I've built many two, three, and almost four-story pole-barns. All worked out fine, passed inspection, etc.
Like anything else, you have to calculate load and stress. You also have to make sure you use the correct type poles and the correct hardware.
Keep in mind that if your treated poles are NOT CCA, and are later ACQ type, you've got to use stainless steel or hot-dipped galvanized hardware.
In your situation, what exactly will be the floor joists-girders, and what will they be attached to? If they are attached to 4"X6" poles, or 6"X6" poles, much depends on their spacing, how deep they are, and what they are sitting on underground.
The girders are what you will be bolting directly to the poles. Then you add joists perpendicular to those girders, and your flooring gets attached to those joists.
If this was a residential structure, it would be more complicated. You'd have to calculate soil density, and add large concrete pads under the poles.
Since you've got more of a farm-use, not so complex. If your poles are spaced 8 feet apart, and you want to add an upper storage area across three poles to span 16 feet . . .
You need a joist-carrying girder a minimum of 2" X 10" if strong #1 wood (larch, Doug fir, southern yellow pine). If a #2 wood (most common framing lumber rated S-P-F), you need 2" X 12".
If you want to run twin girders bolted to both sides of the poles, on 8 foot centers, then #1 wood can be twin 2"X6"s, and #2 wood can be twin 2" X 8"s.
If your poles are spaced 10' apart, then increase all to the next larger size.
Once the girders are attached, you have to figure how long the floor joists will be.
Floor joists spaced 24" apart - a #1 2"X6" can be run a max of 8 feet. a #1 2"X8" can go 10 feet. A #1 2"X10" can go 13 feet. A #1 2"X12" can go 16 feet. If you space joists closer at 16" centers, you can add a foot to each span.
This is the "almost" four story barn I built 20 years ago. Bottom is all 6" X 6" poles spaced 8 feet apart. 2nd full story, attic 3rd story,and a small 4 th story bedroom sticking out the top.
Here's another I haven't finished yet (in the Adirondacks). Pole contruction on the bottom level, and 2" X 6" framed walls on the upper. Poles are all 8 foot spaced. The nice thing about pole construction is one person can do it, if careful. No "work crew" needed.
Here's another. My old farm house built 1820. Added a pole-barn type addtion for bottom,and 2"X6" frame on top. Had to build around an old well that is now, inside our kitchen.
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