Connection limit of 32,767

SQL Server has a hard concurrent connection limit of 32,767.

Without implementing an external caching solution, what is the best approach to supporting a large number of concurrent applications (that require read/write access) that could easily exceed this value?

At this point I have concluded that I either need to implement or purchase a third party external caching solution, neither of which is a simple change.

Thank You,

Bill

William F. Kinsley