I'm surprised they let you have that package (AT100+, Classic Bronze or whatever it is these days) without the locals. In fact, I tried to downgrade to AT100+ and was told I couldn't do so without keeping my local networks (which I am only interested in for the Bengals come football season). I keep the AAD SD networks at all time (both coasts). The mileage you get may vary in regards to the alternate networks but I can confirm that I don't get those even with it being advertised on the DISH website for the package. I don't even get them and I kept the Multi-Sport package.
It won't help you with the Memphis Grizzlies or Nashville Predators (as they are always shown on one of the alternate networks anyways) but I can assure you that if you order the Multi-Sport package, you'll get the Rays and Marlins on the Sunshine Network or FSN Florida. You won't, however, get any of the live professional games outside of your territory. I'm a huge fan of the package, though, and would recommend it at only $5.99 / month. I also enjoy the NHL Network, NBA Television (which I would get anyways as a League Pass subscriber) and Big Ten Network. Everytime I have watched an NHL replay (whoever was against the Maple Leafs) it was in the clear. I also noticed (last season) that I was getting the Denver Nuggets replays so long as they were on Altitude. I enjoy some of the regional shows as well.
Unfortunately, though, I don't think you'll be able to get the Predators or Grizzlies unless you upgrade to AT200 or AT250 (or you won't get the alternates).