It's not that simple, with multiple stories the drains from the upper story have to be kept separate from the vents from the lower story. So any stack that you want to tie into upstairs, you are going to need to run a separate parallel pipe going downstairs.
If you want to keep the existing stack as a vent (simplest conceptually), then you can tie into it for the vent for your upstairs fixtures. But you would run a separate parallel drain from the upstairs fixtures that goes downstairs. It can connect with the existing stack at a point where it's a drain only and no longer a vent, including not a wet vent. If there's wet venting, that might not be on the stack, it might be farther downstream on a horizontal portion in the lower story floor.
An alternative would be to convert the existing stack to being a drain between the stories instead of a vent. Then you'd run a new vent from downstairs and connect it back into the stack above your upper story drain connection. That has the advantage of allowing a possibly smaller pipe for your new parallel pipe, but it may be trickier to figure out.
Either way, I would think it would make sense to only use the 3" stack for the new upstairs fixtures, and tie all the drains together upstairs, rather than dealing with the issues twice, once for the 3" stack and once for the 2" stack. And you will need a complete understanding of the drain and vent piping of all the downstairs fixtures utilizing the 3" stack for drain or vent, so you know how to tie in downstairs.
Cheers, Wayne