Azure VM with many IPs or SSL certificates

(as discussed in comments on the question):

SNI on IIS 8 is a potential solution to this problem, but depends on being able to actually use SNI, which is not supported in the Windows XP cryptographic libraries.

The Wikipedia edit that states that Windows XP SP3 with IE8 supports SNI is incorrect.

Per this Microsoft blog post, it's not present on Windows XP, regardless of service pack:

Unfortunately, SNI support isn’t available on Windows XP, even in IE8. IE relies on SChannel for the implementation of all of its HTTPS protocols. SChannel is an operating system component, and it was only updated with support for TLS extension on Windows Vista and later.

Further, I was able to enlist the help of Journeyman Geek to verify this in the real world, on an XP SP3 system with IE8, using this SNI test site:

So, you can use SNI on IIS 8, but Windows XP clients still make up about 40% of browsers on the internet according to one measurement as of August 2012; it's still probably not appropriate for most public sites.

Once mid-2014 rolls around and XP falls out of support, hopefully it starts to drop off and it'll be much more practical to use SNI.