Parents who share email
I did not see a way to add a second parent to a child who shares the same email address or a parent that does not have an email address but may want their information sent only via text message.

At this time we don’t plan on supporting parents without individual email addresses. It’s important for secure access that everyone have a verifiable individual login. However, you could easily work around this.
You could use a non-existent email address (email addresses at “@example.com” are “safe” in that they will never belong to a real person.).
You could give them an email address at your school just for logging in.
Parents can get a free email from gmail or yahoo and keep it private in the tool, just using it to login.
You could even have one “parent” who’s first name is both names, like “Bob & Margaret”.
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EricW commented
As a workaround, almost all cell phone carriers proved an email address that can be used to send texts to a cell-phone.
This website lists the appropriate format for each carrier.
http://www.emailtextmessages.com
If the parent who wanted text updates only, used that email as their email address and then selected texts as the notification method, would that work?