Could we create a second User Profile Service Application ?

Yes you can but ,
If you have only one server in your farm you can use just one User Profile Service Application (UPA) in this server because the windows Service of User Profile Syncronization Service just configurable only one UPA. So if you have more than one sharepoint server in your farm for example 3 server;  you can create more than 3 UPA but you can only syncronize 3 of them.

For Another scenario, i assume that you have only one server and already provisioned one UPA and configured the syncronization connection. After adding second UPA as you know you can not able to add any Sycronization connection for Second UPA . But if you stop CA-> Services On Server -> User Profile Syncronization Service and restart it will prompt you to select UPA options mean you can change the relation for specific UPA . Still only one UPA can able to sync for one server.