No, but there are alternatives
Sorry for the short answer, but unfortunately, USB just doesn't work like this. Because of... protocol reasons that we won't dive into here, USB doesn't have anything really resembling this capability. The closest you'll get is a standard hub or KVM.
However, what does exist are serial splitters. Since it appears that all you're doing is using a COM port, what you could do is use a USB -> serial adapter, split the serial port into several serial ports, convert the serial back to USB (or whatever you'd like), and proceed to plug those into whatever target computers you're using. If that sounds like one too many adapters, StarTech even the ICUSB2324, a convenient USB to quad serial adapter.
However, there's a reason we don't all have USB and serial splitters plugged into our computers. There's almost always a better way of doing things, unless you're working with specialized, legacy hardware. Networking and virtual serial ports exist for a reason, and you're almost certainly better off using one of those. Without more info on your application I can't really say that with 100% certainty, but it's probably true.