Providing that the old web files are in the same place that they were before you changed the nameservers to DreamHost.
In theory you could use several hosts and have a different website on each and just keep changing the nameservers to point at each one. You would have to suffer the problems of waiting for propagation each time and the problem with email going to the wrong place until it caught up.
In practice you would probably confuse yourself and not know where you were. Much like me most of the time!
Opinions are my own views and are not the views of DreamHost.
Any advice offered by me should be acted upon only at your own risk.