Running VMware in VMware?

We have a physical machine that runs VMware and hosts a VM we use for SharePoint deployment testing. That machine is old and dying, and my employer's network czars are heavily pushing hosted VMs as a replacement for outdated physical servers. I was curious about whether it's possible to run VMware inside VMware, and if so, whether there are severe performance implications. We don't require extreme performance from this setup, since it's just used for SharePoint testing and the associated SQL Server is on a different box. My guess is that we can't just use the primary hosted VM for our testing because we'll want to roll back occasionally and otherwise have more control over it, and getting buy-in for that from the network folks is unlikely. Does anyone have any experience with this?

edit: I know this nesting certainly isn't the preferred option, but (1) we want the flexibility of being able to use VMware snapshots at will and (2) the network folks will not allow us to arbitrarily roll back to a previous point in time because of the potential for removing mandated security updates. My guess is that a local desktop machine running VMware Workstation might just be the way to go. The hosted option seems attractive if it will work though since it's less machine maintenance for me to deal with.