Sharing a single API dns name across varying base path names that represent API extensions

### Describe your idea/feature/enhancement

We need a way to extend an API across different repositories by creating a new base path name for an existing, shared API DNS name. For example:

api.mycompany.com/service1 created in template1.yaml using a single API Gateway and Serverless Function resources.
api.mycompany.com/service2 created in template2.yaml using the template1.yaml API Gateway and different Serverless Function resources.

### Proposal

Our understanding is that is a limitation of SAM but using a combination of CloudFormation and SAM can achieve automation that would achieve a shared api domain goal that supports extensions via basename changes only. This should be supportable via SAM itself.

Things to consider:

Sharing API elements across SAM templates. We are primarily looking ways to simplify maintaining a growing API over time without resorting to creating a unique domain name for each API extension that emerges from collaborating teams over time. Ostensibly,
service1.mycompany.com
service2.mycompany.com
...
is not as valuable as
api.mycompany.com/service1
api.mycompany.com/service2
...

### Additional Details

AWS Support suggested we create this issue as the limitation of sharing a single API domain across SAM templates is a known limitation.