Can you just add more storage for ten dollars or less per month?

Umm, I'm a little confused here.

I assume you're talking about iCloud Storage. If that's the case - great news! you're set!

There are three tiers of additional storage:

50GB for $0.99

200GB for $2.99

2TB for $9.99

All three of these options are 'less than $10' a month (at least in US pricing - other countries may vary)

iCloud+ plans and pricing - Apple Support

You cannot add storage to your iPhone’s internal storage for any price; it will never have more than it did when you bought it. You can “rent” iCloud storage on Apple’s servers for backing up and for syncing.

See→What's the difference between device storage and iCloud storage?

You can 'rent more space' in iCloud by following the details in the link I posted above.

As noted, though, it won't directly give you more space on your device, but you can configure your phone to automatically offload idle data to your iCloud storage, indirectly freeing up space on your phone.

Not on your phone, as I explained. Only in iCloud, which will not add any storage to your phone.