A no-hub connector (Fernco makes some) would be used. But, you'd need to revent the lower floor. Using it's vent as a waste pipe changes its use from a vent to a waste line.
There has been some discussion about inserting PVC into a cast iron vertical stack. If I remember, it is not allowed in some places. The considerable weight of the CI might have long term problems on the PVC in the middle. They do make no-hub CI bits, then you could transition to pvc for the new horizontal stuff, if that's an issue. You'd crack out a section of CI, insert a new Y in CI, then transition to pvc.