If there are multiple changes at the same time in the same account or shared folder, you can run in to this 'too_many_write_operations' error, which is "lock contention". That's not explicit rate limiting and can't be increased or removed; it's a result of how Dropbox works on the back-end. This is a technical inability to make a modification in the account or shared folder at the time of the API call. This applies to all account types. You can register another account, but that account would also be subject to lock contention.
This error indicates that there was simultaneous activity in the account or shared/team folder preventing your app from making the state-modifying call (e.g., adding, editing, moving, copying, sharing, or deleting files/folders) it is attempting. The simultaneous activity could be coming from your app itself, or elsewhere, e.g., from the user's desktop client. It can come from the same user, or another member of a shared folder. You can find more information about lock contention and optimizations you can make here. The app will need to be written to automatically handle this error.
In short, to avoid this error, you should avoid making multiple concurrent state modifications and use batch endpoints where possible. That won't guarantee that you won't run in to this error though, as contention can still come from other sources, so you should also implement error handling and automatic retrying as needed.
I recommend referring to the error documentation and Error Handling Guide for more information.