This actually depends on your hardware, your software, and your infrastructure and is not actually governed by Synergy at all.
SQL Server
If using Microsoft SQL Server as the database back end, the maximum number of concurrent connections is 32,767. However, this figure may be limited by the version of software, by your hardware, or by your network infrastructure in general which may not be able to handle that many connections.
In addition, Synergy may need to open more than one connection in order to perform certain functions. This would be a rare scenario but it is possible. For example, if you check or modify data in a custom database held on the same server instance say in order to include information from two or more companies in a group or to retrieve address information from a separate database then you would need to connect to two or more databases which would use up two or more connections.
Standard Database
The standard embedded database supplied with all editions of Synergy can handle multiple connections, but because it is a file based database Windows file and record locking has to be used and the nature of this limits the number of users. This is completely outside the control of Synergy and of the database engine itself, and is part of how the operating system works. As a result the more users you have the slower the database access can be.
Important: Because of the way Windows file and record locking work, the speed will not go back to exclusive use rates after having more than one computer connected until ALL connections have been closed. You can do this simply by selecting File | Close from the main menu and then simply re-opening and logging back into the database.
Options
You should never have a problem with an exclusive single machine connection whether it is to a local database (stored on your machine) or a remote database (stored on your server, NAS device or other network attached storage) but using more than one concurrent connection can cause a noticeable slowdown in the transfer of data.
In other words, if two computers share the same data but never at the same time, then there will be no issue. If you need more than two concurrent users then you should consider using Microsoft SQL Server as your database back end. Synergy supports both the Full and Express editions of Microsoft SQL Server 2012 onward.