The real ones who can answer that are the folks at your municipality. They know your local code requirements.
In my area your plan would not meet code. Minimum floor joist size, no matter the length, are 2x8ís. Even then, maximum clear span would be only 10 feet.
You might be able to get away with using laminated beams, sistering one next to every other 2x6 you have in your floor. That might get to be expensive.
Again, your municipality would be the best source for what you can and cannot do.
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