This documentation is for Taxamo v1. If your account is with Taxamo v2 use the documentation at integrate.taxamo.com/doc.
If you are uncertain of your version please contact support@taxamo.com for assistance.

Can I register for MOSS in more than one EU Member State?

That will not be possible, as soon as you register for MOSS you pick your Member State of choice (any one of the 28).

You cannot apply for MOSS in multiple jurisdictions – it is a one-stop shop.