The client wants us to incorporate that into an existing schedule, combining the two. If we did that, would the original baseline dates be changed to match the actual start/finish dates? Is there any way to maintain two separate sets of baseline dates within the same schedule?

If we make a copy and restore the baseline for the original project and you copy/paste WBS-es from the new project into the old one. The problem might be the data date in the baseline may be different than data date in the new project.