The problem with running multiple audio interfaces simultaneously is that the drivers typically won't work. Even if they do, audio applications often are designed to work with a single interface at a time. If you are running OS X, you can aggregate audio interfaces together to appear as a single large interface.
The problem with aggregation, either using OS X's aggregation interface, or a vendor's driver is that it is tricky to synchronize all of the audio interfaces.
The other problem is that most inexpensive USB audio interfaces are running the USB at the slower 12 Mb/sec rate, not the faster 480 Mb/sec rate. The problem with this is that once one device slows the USB bus down, it slows down for everyone else (unless you have an exotic hub that allows streams of multiple speeds to coexist. These are hard to find, so you probably don't have one. I do, and I'm not convinced it actually works as advertised. It certainly didn't make my Virus TI happy). So even if you could get a bunch of cheap USB interfaces to coexist, you'd end up with fewer ports than if you just bought a bigger Firewire or 480 Mb/sec USB interface.
From a software engineering perspective, you want to transport audio in large blocks from the interface to your application. But large blocks of audio means greater latency, and that is the opposite of what you want as a musician. So you need to find a happy medium between those two points. When you are running multiple interfaces together, the 'starting' time of the blocks coming form each interface will be different, and not all hardware provides a mechanism to synchronize those blocks. So you may end up with a lot of jitter in your recorded audio.
For best results, pick an audio interface that has the number of ports you need and go with that. Some vendors (like MOTU) support multiple interfaces, so if you need a very large number of channels, pick a vendor that support expansion.
If you are trying to save money, consider buying a used interface. However, beware that not all vendors are good at providing drivers for their legacy products. I've been very happy with my MOTU 828 mk2 on my mac, but that may not have enough ports for your application. Also, the early 828s were Firewire only, which may or may not be a problem for you.