You can run two different versions of Sitefinity under the same IIS. Please read this article
in the documentation which talks about creating and running projects on IIS. After that you need to configure
the IIS in order to host the projects in SItefinity.If you use the ProjectManager.
When running different versions of sitefinty that are running on different versions of .NET framework sitefinty 3.7 have versions supporting .NET 2.0, .NET 3.5 and .NET 4.0 while sitefintiy 6 supports only .NET 4.0.
Having the above in mind if sitefinty 3.7 is running on .NET version that is different form .NET 4.0 (here
is an article how to check you sitefintiy version) make sure to have separate application pool running in .NET 4.0 for sitefinity 6 site and another application pool running .NET 2.0 or other for sitefinity 3.7 sites this way there will be no problems (here
is a screenshot).
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Public Issue Tracking
system and vote to affect the priority of the items