plumbers,carpenters, need some help

First of all, get yer Sawzall, you need it for this job. Then cut next to the joist, don't try to ride the joist 1/2 on it. You can add a rail attached to the side of the joist at the height you need to only use one layer of 3/4" plywood for your patch. Geof

I have seen it done that way but it allows a bigger area for water penetration and it is never as solid as the flooring being put on a joist unless you can put a full length board from support to support in there. Water is your enemy here. A friend of mine had to rip his floor up and redo it because the inspector flagged it when he sold his house.