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Perhaps you could make use of different workspaces if you have multiple clients you work for, so you can have one Clockify account with multiple workspaces on it.
They all just need to invite you to their workspace and you simply switch between workspaces depending on the client you work for at the moment. This way there wouldn’t be a need to have multiple accounts.
Example: I have one Clockify account with example@personal.com email address. I work for clients: A, B, and C. Each of these clients have their own Clockify accounts - therefore, they all have their own workspaces and they invite me to join and track time in their workspace.
Now I have access to these workspaces and can track time for my clients in their respective workspace from my personal Clockify account. Neither of them will be able to see what I tracked in a different workspace since workspace are designed to be completely separate.
You can find out more about workspaces here.