Do multiple SPs from the same server each need their own public/private keys?

[Cody Carmichael]

If I have a software product that runs on a server, and this product
consists of multiple services that provide their own login to a user, does
each SP need its own public/private key pair? Like for example, if I have
the following servers:

https://mySP.awesome.net
> https://myOtherSP.awesome.net


So the first server has the following sources of metadata:

https://mySP.awesome.net/rest/v2/sso/messege/shibboleth/metadata
> https://mySP.awesome.net/rest/v2/sso/admin/shibboleth/metadata
> https://mySP.awesome.net/rest/v2/sso/mobileclient/shibboleth/metadata
> https://mySP.awesome.net/rest/v2/sso/othermobileclient/shibboleth/metadata


And the second server would have the same. For each server, does each SP
need its own unique public cert in its metadata or can the SPs on one
server share just one public/private key pair?
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