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The maximum number of connections across SQL Server versions and editions is 32,767.

You can determine how many connections SQL Server currently has by looking at:

SELECT ConnectionStatus = CASE WHEN dec.most_recent_sql_handle = 0x0 
        THEN 'Unused' 
        ELSE 'Used' 
        END
    , CASE WHEN des.status = 'Sleeping' 
        THEN 'sleeping' 
        ELSE 'Not Sleeping' 
        END
    , ConnectionCount = COUNT(1)
FROM sys.dm_exec_connections dec
    INNER JOIN sys.dm_exec_sessions des ON dec.session_id = des.session_id
GROUP BY CASE WHEN des.status = 'Sleeping' 
        THEN 'sleeping' 
        ELSE 'Not Sleeping' 
        END
    , CASE WHEN dec.most_recent_sql_handle = 0x0 
        THEN 'Unused' 
        ELSE 'Used' 
        END;

If the ratio between used and unused connections from the above query is concerning, it is likely that connection pooling is enabled by client applications connected to the server, and those connections are not being efficiently used. You may want to have developers modify the connection string for these applications to limit the size of the connection pool, and ensure they are properly disposing connections. If connections are not being disposed correctly, they will remain open as long as the client application is running.