Currently office.com seems to default to the last used account type witch is fine except there is no way to manually change what side is active and you are forced to actually browse to the business site manually via some direct link or vise versa (if you happen to remember/have bookmarked a suitable link like outlook.com for example). Not good.

This is also directly related to the many complaints about how badly Office 365 handles using different business accounts at the same time.

There should be an account selector in the top bar, on the business and personal site.

Sure, this can be circumvented with browser addons like Firefox's Container Tabs which basically launch separate instances with their own cookies and other **** in the same browser window but this is not how commercial services like Office 365 should be used. This is really something that Microsoft should invest in. Google makes it relatively easy to use multiple accounts at the same time and changing between them is also simple enough.