There has been talk of PostGres support for vtiger.
vtiger does support it partially as of now.
PostGres support is a work-in-progress and Jens Hamisch is the person who is primarily responsible for the work. Allan Bush was working on it earlier. Thanks to these people, vtiger is able to even state that it has partial support.
The contributions will be integrated into the trunk sometime down the line. In the meantime, you could contact them or access their branches to use the feature.