No.
We cannot expand an individual's space in our Google Workspace accounts.
Well then how do I manage the space I do have?
1. You should never have anything in your email that cannot be deleted.
This is the biggest factor. Images, videos and emails themselves will eventually take up a log of room. Make sure to go through your emails and save images to the proper folders, and if an email is important, download the email and save it to the drive. Again, you should be able to delete your entire inbox, and not lose any data!
Well, if I move everything over do the Drive, doesn't that take up just as much space?!
Yes! But here is point number...
2. Your folders that take up too much space should be transferred to the ownership of the Admin account.
You will still have access to those items, the difference is, it won't take up your personal space!
There is no other way! I promise that if you follow this, you will have all the space in the world!