With cable you are only paying them for one connection, you can physically connect a second modem, but it will not work as the cable company will have security measures in place to prevent this. Otherwise anyone would just take thier lowest service, and connect what ever they liked to get everything.
You should use the Ethernet port on any cable modem, it is a lot faster.
If you need more speed, check with the cable company and pay for more speed from them. If you are already at the highest, and still need more, then pay for a second line, and dedicate that to the PC that needs it. Connect the new cable modem to the second nic card, and configure the PC as normal, but remove the default gateway IP address (which is probably the other modem, or a router) from the original nic card, then everything for the Internet will use the new connection.
If you need to allocate more bandwidth of your existing link, to one PC over the other, then you can configure some routers to do this. It is a bit complicated, so ask if you want to go down this route and we can post more information.
I don’t know where you are in the world, but here in the UK the cable comany offer 50Mbps as the top speed to most areas covered, and 20Mbps elsewhere, that should really be enough for any ‘home’ user.