Through the hosting account and VirtualHost, you can map any domain or sub-domain to any server sub-folder. For that domain, its sub-folder will appear to be public root. Its true server path may be public_html/example.com/ but to all outward appearances it’s as though example.com’s core files are in public_html.
I don’t think there’s any reason to purchase a third domain simply so the existing ones could be mapped to its network. Only do so if the third domain has some desirable marketing or promotional purpose. What I recommend depends on whether you will stay with a network concept or just use to independent single sites on the same server.
You can assign a new sub-domain to either existing domain and map it ((in hosting, not multisite)) to a sub-folder to use as a staging site on which to develop the new sites. This will work for either network or single sites. When the time comes to launch, convert the root folder installation to multisite if it is not already and that is what is desired. Update its wp-config.php to point to the staging DB that will become production. I’m assuming here that the current sites are also WP based. If not, the site will need to be down for a short time to move files around to effect transition from old to new.
Do a search/replace on the DB to update all staging domain references to be production instead. If you decide to keep two single installations, you can re-map (again, in hosting, not multisite) one production domain to what was initially a staging sub-folder. Again, update the staging domain references in the DB to become production.
Personally, I don’t like developing on a staging site, I much prefer to develop locally. The main drawback is clients don’t have access to my local environment. I will need to migrate everything at some point to a staging site for client approval prior to launch. For launch I either migrate again to production or re-map the existing production domain to the new site’s current staging sub-folder through its hosting configuration, in essence altering VirtualHost configurations.
This probably all sounds horribly complicated. It really isn’t, but it’s difficult to explain. If you’ve not done this sort of thing before it can seem overwhelming. Once you look back after having gone through the process I think you’ll agree that it really isn’t that complicated.