You can create a new Google account to access the Google suite of tools using your existing email address. The only Google app you’ll not be able to access is Gmail, which is fine because your email is already managed elsewhere.
Direct your browser to https://accounts.google.com/signup. (NOTE: As recently as 3/14/17 some users are getting an error "The page you've requested is invalid." error. If this is the case, please try a different browser or use Incognito Mode in Chrome or Private Mode in Firefox). Click "I prefer to use my current email address". This changes the form slightly. Enter your current or personal email address and follow the on-screen instructions to create your account.
To use a Microsoft account, go to https://account.microsoft.com/account, then click "Sign in With Microsoft". Then choose "Create Account" and provide any email address you like.
Facebook too will provide as authorization. Head to www.facebook.com and sign up using the fields shown below, using an email address of your choice.