First, you shift the piping for the forced hot water system, which is being replaced, but is still necessary.
When I envisioned building the form for the bridging slab, I figured a piece of plywood would lie across the top of the piers, have sides, and be filled with rebar and concrete. But I couldn’t figure out how you would get the plywood out from under the slab. Well! Guess what! One builds several bottoms, between the piers, that can be pulled out in sections. I am impressed.
First, you frame each bottom section by dropping the frame the width of the plywood, so the whole bottom seems smooth and seamless, (and you could say you just put down a piece of plywood and easily got it out from under after the pour).

The bridging span extends over the end of the stairs to the basement and rather than have the access too restricted, we substituted lolly columns for one of the concrete block piers.
The Building Inspector approves!

And tons of stuff gets delivered.