The contents on the Office 365 start page are driven and managed by Microsoft Graph. Contents are personalized to the individual user’s recent activities and customized quick access.
Per my knowledge, there is no option to customize web parts on the Office 365 start page. It's by design.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.