I am continually logged into two Google Apps accounts on my normal Windows computers using Chrome and on my Chromebook. It is a lot more difficult and non-intuitive since Google went to their converged account implementation.
Since you indicate that you have had multiple accounts open at once, I assume you have activated the multiple sign-on function. Since Google Apps logons are cookie based, it doesn't matter if you have multiple windows or tabs of the same browser, they all use the same cookie repository.
In my PCs, I use multiple instances of the Chrome browser. In my Chromebook, I just use multiple tabs in the same browser window. I also keep the Contacts for both accounts open in two additional tabs.
Sign into one account, as normal. Then sign in again on another tab and it will bring up the same account as in the first tab. Then, go up to your account name (e-mail address) near the gear in the upper right corner and click on it to open up the dropdown list. Click on switch account (or sign in to a different account, whichever is shown). Either click on the other account name, or sign into that other account. I find that I always have to do the switch account thing twice to get the account change. The first time it just reloads the account that I was in.
That should get two accounts open. Just do the same thing for the third account (in a new tab).
The process is way more cumbersome than it was before, though now you can get to more applications with either account, which is what the change was all about. Hopefully the large customers will force Google to redo the implementation to something much more usable.