Theoretically, you can just solder another on. Practically, the chances of doing it successfuly are not good. There are 19 tiny solder connections to make, and there are other considerations.
There are HDMI field termination kits. The ones I have seen are designed for ribbon cable or 28/30 AWG round cable. There are also HDMI screw terminals. And there a HDMI splices. However, even if you can make the connection, performance will suffer. If you are not pushing the ragged end of bandwidth, one of these might work for you. Worth a try if you really have no other option, I guess.