Yes, although for practical purposes I believe most counts only keep an ace side-count.
There's "levels" of count -- if basic Hi-Lo has all of the tags as +1/-1/0, that's level 1. If you use a count that marks A as -2, 5 as +2, and otherwise uses the Hi/Lo tags, that's level 2. I believe there's a variety of upper level counts developed by Wong, Uston, and Revere that a simple google identifies -- most of these have As and 5s as the upper-most tag in the count.
Keep in mind, if you read up on some of the older threads on here, that there's a practical matter at work here -- card counting is only effective if you do it pretty much perfectly (probably averaging one counting error every 5-6 shoes or so, and never making any play errors). Adding complexity reduces the chances of you being able to count perfectly in a casino environment (filled with noise, smoke, and pit bosses). So if you can keep regular Hi-Lo perfectly, and earn 80% as much as you would with a more complex count, you may be better off -- both in terms of heat and variance/EV.