More than one stem indicates that they are multiple plants. They would be very hard to seperate them from each other. Pinching off tops is not necessary until they start to send up flower stalks as you stated. If you can seperate them with no damage to fine roots, you might be OK. I avoid buying store bought, as thats one of the reasons I don't like them due to crowding. They tend to have more plants in a single pot. Clumped together, they will all be stunted a little. On the other hand Cilantro is great when clumped, as is garlic chives and some others. Basil, has many varieties, so you also need to know what kind your growing. There are red leaf, lemon, pineapple, and so many other flavor variables, that store bought is just a guessing game.

I just planted a whole nursery pot of a many-stemmed bundle into a larger (16") fancy pot for pretty; it will make a nice, full display. This bigger pot sits on a 3' stand and gets morning full sun and afternoon bright shade..... while basil likes heat it doesn't always love a whole day of our California sunshine. The reason it is on a stand is so that I get to harvest it instead of my 4 footed friends. I make sure I feed my potted herbs right along with the flowers and never have any problems with any growing and being tasty.

Separating basil seedling is easy;
I always say; If they can transplant human hearts, you can transPLANT A PLANT!? Here is how I would do it.

1- water the pot real thoroughly.(They get all the water and food they need before surgery!)
2- prepare the spot for transplant.(Individual holes, spaced accordingly)
3- Take the whole thing out of the pot.
4- if they are not completely attached, brake them apart at the open area, with least disturbance. If almost attached, put them in water a while. Take them out and separate then by gentle force(pullin apart) and some shaking.
5- Put each in a hole(you had it ready before separating), while holdding it upright with one hand, pour soil around the root, pack lightly.
6- Water gently immediately as each planted(with a cup or similar container) to the point that it is flooded. If the plant leans, straighten it up and pour more soil around it, water it one more time.

7- do same for each transplant.

I WOULD DO THIS IN LATE AFTER NOOn,OR IN A CLOUDY DAY TO AVOID HOT SUN. THE PLANTS WILL HAVE A TIME TO GET OVER THE SHOCK OVERNIGHT.
THE FOLLOWING DAY WATER THEM, OR BETTER YET MIST THEM WELL COUPLE OF TIMES. THEY MAY LOOK KIND OF WILTING BUT DO NOT WORRY, THEY WILL GET OVER IT.

I have separated my basil plants without any problems. When you pinch off the tops, go to the next set of leaves. Pinching them will make them bigger and bushier. Definitely need to keep pinching the flowers once they appear. Some of the other varieties of basil, lime or spicy basil, don't flower as heavily as the sweet basil does.

Thank you for the tips!!!!
I really do feel that the two pots need to be separated more. I know when I have grown basil before, I don't remember so many stems!
Cyrus Gardener thanks for the "surgery tips"!! I plan on trying my transplants tomorrow, when it will still be somewhat cloudy and cool, but on the way to warming up! I figure if it doesn't work, I will just go back to the nursery I bought them from and get more! ;)
As for pinching off the tops, I so want to do this now!
I have a great new recipe to try for tomato tartlets and I keep thinking how good the fresh basil will taste on top!
Westelle- your pots remind me how last year I planted one basil plant in a big planter. We lived in town, with so many trees around our house, that all summer we dragged that planter all over the yard to get enough sun! It did very well, at the end of August I completely stripped the plant and made enough pesto to feed me, hubby, 5 kids with assorted spouses and children for at least 2 meals! I love the idea of container gardening!
Thanks again everyone! As soon as I get organized I will take before, during and after pics!