@Jakub Albrecht, Thanks for posting in Q&A.
Based on my experience, when there is app protection policy applied to corporate outlook account, other account cannot be added on the same outlook anymore.
To clarify this issue, please check the following.
1.Are these three corporate accounts belonging to three different tenant or one tenant?
2.Please check If there exist app protection policy in Microsoft Entra or Microsoft Intune.
Please check above information, if there is any update, feel free to let me know.
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