Yes, but this isn’t exactly a plugin type simple solution.
If you’re running out of database space on your present server you might want to move your database by itself over onto a bigger, better server.
I recently migrated a multisite’s database from a shared host to a VPS host while leaving the multisite itself back on the shared host. Pretty simple and easily freed up the shared host to run just the WordPress itself while the VPS took over the database allowing a good bit of growth before I’ll need to change much else.
The cool thing is you can run a fairly large multisite WordPress from a shared host and a simple VPS as long as your traffic, themes, plugins, and media files don’t tax the shared host too much. You can toss in an assist from something like CloudFlare to pick up the slack.
There are other solutions but you’ll need to pursue those on your own or hire a developer who can build that out for you.
