South Fla... batten down the hatches.....
You have to insert a NEW instance of Cakewalk Sound Center (CSC) for each new part you need. One for bass, one for piano, one for pad, and so on. Drop the appropriate midi parts into those tracks and select the instrument patch/sample.
If you are inputting the midi from a keyboard or a controller, you should disable the input of the other midi tracks so they are not playing from the streaming midi. They will automatically play the midi from the track only ...if you have disabled the input. Otherwise, say you solo a track and play it back and at the same time are playing the keyboard..... you will hear the recorded stuff from the track AND the new live stuff as well.
Depending on the computer, it's memory, speed, and the sound card or interface you are using.... there will be a limit to the number of CSC instances you can add, and have play back in real time without running into latency and out of sync track issues. With a factory sound card, this number is generally quite low. An aftermarket USB music interface will allow the limiting factor to be the computer and the software, not the sound card.
Actually thinking about it, the sound card, if it is a factory card, can very often cause all sorts of strange things to happen when it comes to the sound. It's not clear in the OP if you were using separate instances or not. If you were, it is very likely the sound card. A factory card likes to use MME drivers. You can also up the buffers a bit to let it have some breathing room.
The best option is to get an inexpensive audio/midi interface to use as the sound card rather than the one in the computer. That will use ASIO drivers and generally resolves these sorts of issues.
Anyway, hope that answers the question.