Updating Plugins on Staging copy of WordPress site

We're updating WordPress and a slew of plugins on a client's WordPress website. We made a staging version of the live site. It has a different URL than the live site.

We've updated WordPress and all the other plugins on the staging version of the site from within WordPress.

We can't update your plugins (WPMU DEV Dashboard, and Google Maps by WPMU DEV) from withing WordPress . We suspect that it is because the staging site has a different URL than what is registered with you for the live site?

Our goal is to update everything on the staging site, test it all, and fix anything that breaks before pushing the staging site to replace the live site. Please let us know if there is a way that we can achieve our goal?

Thanks.