Yes and no.

You can do that with a new installation of WordPress into https://www.sitename.com/secondsite and then importing the data from your localhost.

You could also turn the current site into a multisite but I think your second site would have to be a subdomain (like https://secondsite.sitename.com) instead of a subfolder (like https://www.sitename.com/secondsite) because it would be a conversion to multisite rather than a fresh multisite install.

But, for both options you would need to have access to the hosting space and database (via FTP and PHPMyAdmin, for example, or the Control Panel) in order to do the installation or conversion.

thank you for the response. I thought that may have been the case. Thanks for confirming. I run our local site on a subdomain of a global domain already so the second option would suit.

Back to the drawing board ??

Thanks again