FYI - ETrade does not allow 4 decimal place trades except for stocks listed on the pink sheet that trade below .01
You can call the broker directly and place a 4 decimal trade but there would be little point since you then pay the assisted trade commission rate.
If you place your sell at say .38 and the bid is .3801 you will get filled at .3801 until those shares are depleted. Same on the buy side.
Considering so many trades are 100 share in the fractionals, I tend to agree with the boss that these are not retail traders. But I also don't think they are institutions. I think they are MM efforts to keep liquidity trading to each other. That is one of their jobs in the markets.