Hi Piotr,
Based on your description, do you mean you want to use OneNote for Mac with your Office 365 account? If so, you can directly sign in to OneNote with Office 365 account by clicking the down-arrow> Switch account in the upper right corner.
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What do you mean about ‘sign up using my "corporate" account it says it cannot vfind proper O365 subscription’? Could you please provide us with a screenshot regarding this scenario?
If there is any misunderstanding, please correct me.
Thanks,
Dunk