I had the same problem, and found that you need to change the email account to "Signatures on this device" to see the rest of them.

MarieB315's helpful instruction above solved it for me. Unlike others, I didn't have any problem with editing and saving the signatures on my device (PC).
What was still annoying, however, was that most of my signatures were on the device, but a couple of them (default plus another I had added) were on 365. In case it helps anyone, here is how to solve that problem. It is a bit laborious, but worth it for long-term ease of use:
- Go to 'Signatures on this device'. Select the signature that you want to copy to 365. Then copy the TEXT of the signature.
- Switch back to signatures on your email account. Select 'New' signature and give it a name. Note that the name must be different from the source signature on your device; otherwise, you'll get an alert that 'signature already exists'. I simply added '(1)' to the new signature names, eg: Gordon professional (1). Then paste in the text of the signature from your clipboard, and hit save. Done!
- Repeat this process for each signature you want to transfer across to 365.
- Once you are finished, you will have a number of duplicate signatures showing in Outlook. To get rid of the duplicates, go back to 'Signatures on this device' and delete all of the signatures you have copied across. To tidy up further, you can then go back to your email account signatures and rename them to the original name. Now you have all your signatures in one place, accessible and editable right away.