JMS does NOT provide any Synch as it directly share the MySQL tables.
So I can not guarantee that the bridge will work properly between several installation.

In general, external application have their own database convention to install their stuff and in general you can not have several website in the same DB with independent ELGG ro other extension.
As soon as they use their own "table prefix" they are frequently shared between all the websistes present in the same DB.
The idea that we can not guarantee is to use the JMS joomla user sharing to share the users between all the websites of the same DB and also install you "bridge" to syncrhonize the info with the external extension.

All I can tell you is to test it but I can not guarantee that the sycrhonisation between all the slave site and the external extension will work (probably but not sure).

Thank you once again for your prompt response... They are separate databases and I am fine not having them share a database... I just want a single logon... which can be accomplished... it is called duo logon for the Jfusion project...

For now, I would like a Joomla to Joomlas (Master to 3 Slaves) single logon where once they login into the Master then the slaves will have that user logged in when they click to enter the slave joomlas... so there is no re-logging in... Each Joomla installation will have different content but the same look and feel... It is a functional requirement for this approach...

If your solution can provide that then I am a happy camper! I can work on the bridging of the other applications....

It is not possible to have a single sign-in without sharing the users.
With JMS, you have to start sharing the Joomla user that also share the session in aim to benefit of the single sign-in.

If you don't want to share the users, you can try to install JFussion. It is defined in JMS tools.