(Disclosure: I work for Google, but on nothing related to login.)
Google has supported multi-login for many years: you can log in to multiple accounts, and switch between them. Unfortunately, you can use only one account at once.
I would like Inbox (or Gmail) to be able to show me new mails across all accounts, like the Gmail Android app can show. Or third-party native apps can, like Apple’s Mail app. It’s ironic that Apple’s app works better than Google’s first-party web app for this.
This extends to contacts: I want to see all my contacts without having to worry about which account they were stored in. Or Calendar. Or starred places in Google Maps.
Google search shows me private data like mails in Gmail, if they contain the information I searched for. That should also work across accounts.
Any search box in any Google property should find stuff in other accounts if it’s not found in the primary account. If I’m Google Docs and search for “Vacation Plan”, I want to see my vacation plan no matter what account I happened to be using at that instant. Don’t make me take unnecessary steps like switching to another account and trying to search again. And then closing a redundant tab. This kind of unnecessary navigation is a waste of time — it doesn’t help me achieve my goal, which is plan my vacation. That’s all that matters.
Google should take the next step and bring in data from multiple accounts when you use multi-login, reducing overhead and saving time.