Yes, 10 conductor RJ45 connectors do exist. They're called RJ45-10. Among other things, they're used to connect monitoring cables to APC uninterruptible power supplies. The same connector is used for simple (dumb) level based signals, serial (smart) communication and USB. According to APC, this particular UPS only supports USB, and they still fail to use a standard USB connector.
So, here's how I made an RJ45-10 from an RJ45-8. The metal for the side connections is from an RJ45 jack. Behind the connector you see a temporary connection to a USB cable.