Overpassing O365 sent emails limit

These limits are described in the https://technet.microsoft.com/en-GB/library/exchange-online-limits.aspx#RecipientLimits and that indeed is 10,000 recipients per day, as well as a 500 recipients limit in any one email and if using SMTP client submission 30 messages per minute are allowed. 

Ther is this caveat:

"Exchange Online customers who need to send legitimate bulk commercial email (for example, customer newsletters) should use third-party providers that specialize in these services."

I don't think there is a way to override those limits, as there in place to prevent spam and conserve resources.  A company like SendGrid would be an option or something purpose built to handle this amount of email sending.