Intellectual Property in Network Design

Actually Bill... I have two (conflicting) perspectives as I said.... but to

1) A customer asked 'Can you make sure we have the IP for the network
design' which I was wondering if it is even technically possible....

I think they mean "we don't want you coming back and trying to make any
claim on us for anything we may do with the work you did for us" that
may mean something like they extend it or roll out some more to the
same design or start selling it as part of a system to their customers

There's been legal cases with architects designing a store building for
a chain and the chain then reusing the desing for more sites. I've not
heard of it for networks and your customer wants to keep it that way.

2) If I design some amazing solutions... am I able to claim IP.

Doesn't matter but if you did they want the rights to it already