RHEL 7.3 registration / subscription problem

I know that there's a 6.2 thread for this below - but I couldn't see how the solution applied to 7.3, so please bare with me (especially as my limited Linux skills haven't been exercised for five years!)

I successfully installed RHEL7 on my first PC (albeit after overcoming several pratfalls), and I thought it was all going swimmingly on my second PC. But no. I'm failing with subscribing after registering (and even forcing a registration) as follows:

[root@dhcppc9 ~]# subscription-manager register --username xxxx --password xxxxt --auto-attach --force
The system with UUID 78c4c4ef-4619-473b-b550-22832f4eb9fe has been unregistered
Registering to: subscription.rhsm.redhat.com:443/subscription
The system has been registered with ID: a97c776c-eb51-4360-a3b8-b1f5xxxxx

Installed Product Current Status:
Product Name: Red Hat Enterprise Linux Server
Status: Not Subscribed

Unable to find available subscriptions for all your installed products.
[root@dhcppc9 ~]# subscription-manager list --available --all

No available subscription pools to list

I'm doing something dozy, I'm sure. Or can I only have a single system subscribed to a given customer portal user?

Any help much appreciated.