I'm surprised to find that Apple's OSX Server (Mavericks) ships without TLS 1.1 or 1.2 support.
Are these not widely deployed? Or no sense of urgency since 1.0 isn't broken.
On the other hand, it wouldn't be too hard to build and install a version of the SSL module compatible with the system Apache linked against a newer OpenSSL version, however, and I wouldn't expect this to break Apple's services, at least not until you install an update that either breaks binary module compatability or clobbers your tweaked module configuration.
I don't use Homebrew, so I couldn't tell you if it's capable of building modules for the system Apache, but building the SSL module "by hand" for system Apache with Homebrew OpenSSL should be straightforward enough.
If I was inclined to download and compile libraries then I'd clearly be better off running a linux distro for complete control.
Interestingly Wkikipedia says that TLS 1.1 and 1.2 only have about 25% adoption on servers. Which is shocking if in fact TLS 1.0 is truly broken.
And, if you're curious about client-side SSL support in general, every server test page simulates about 20 most popular (or important) clients. Scroll down to the "Handshake Simulation" section. If you click on client name you get the full-page client report. https://www.ssllabs.com/ssltest/analyze.html?d=www.ssllabs.c...