Add another mic - any mic will do - on the bottom side, pointed up at the snares. Try to mimic the placement of your top mic.  Now the most important part -- you'll most likely have to reverse the polarity of the bottom mic (as always -- use your ears to decide what you like).  I usually use two 57s, bring them both into the console and blend them to the same track.  Make sure you get the blend how you like it -- unless you print to 2 tracks, you can't go back. Pay attention to the sound as you phase flip the signal -- train your ears to notice any cancellation.  This ability will pay off greatly, and it is especially important mixing drums.

Try this technique with toms -- especially the floor -- loads of bottom.  Also works with open-back guitar amps.  You get a nice, round, full addition to the front mic.  Mix to taste.

Hey, Mikey, could you go into more detail on the polarity thing?  I'm not sure if I'm with you...

Would an ambient room mike behind the kit help that snare rattle any?

not this

Also, before some dork corrects me, phase and polarity are not technically the same thing, but in every studio in the world, they are used interchangeably.  If you're into the technical stuff, read this.  Personally, I don't care why something is, just how it sounds. To make it simple, just picture the guitar amp scenario above.  When the speaker moves to make a sound, it initially moves forward; the sound hits the mic element and 'pushes' it in the same direction.  Now imagine the mic placed behind the speaker -- it's element is being 'pushed' by the reverse speaker motion -- picture the opposing mics in a push-pull situation.  If you heard both mics, you would easily hear what is happening -- the same sound is hitting the mic elements at different times (and/or in reversed polarity).  Since you have the same frequency information hitting the same place at different times, the waveforms don't line up and some frequencies are 'cancelled' out.  That is the difference that you hear.

Now, if you flip the polarity of the back mic (if you don't have a switch at your mic pre, you can get XLR adapters to do the same thing), you have effectively reversed the reverse and both signals are aligned.  Got it? Now imagine a second front mic, just moved back about a foot or so.  You have a similar situation -- the same signal hitting the mics at different times -- the two signals are out of phase.  Now do you see how important this is to miking a drum kit with multiple mics?  The same sound hitting seven or more mics at different times could be really messy...and sound like crap.  Condition your ears to hear the difference -- this is one of those things that separate the pros from the hacks. 

Are there other scenarios where we're going to intentionally move the mics out of phase?

 Hey, am I out of phase?

With these examples, keep in mind that even though you may be phase flipping the rear or bottom mics, you are actually bringing it into correct phase relative to the front or top mic.  So, you are not really moving the mic 'out of phase,' you are bringing it closer to 'in phase.'  If you like the out-of-phase sound, that's fine.  You really need to be able to hear the difference and recognize phase issues when you hear them.

"Hey, am I out of phase? "

Actually, you are in a state of reversed polarity.

The guitar player was using a Fender tweed with an open back, so I tried it on the guitar too.  I like this trick!