Well, you don't say where you are, so answering your question is not possible.
In the US, the UCC generally governs these situations, possibly modified by your account agreement.
Even in a worst case scenario, where the payee line says "payable to A and B" (rather than "A or B") or is legally interpreted as such (under the current UCC in force in most states, "and" is the default interpretation), the check becomes bearer paper once both payees sign it. No magic words are required under the law.
Once both payees endorse it, the drawee bank must honor it, and is liable for damages if it fails to do so. (there's a nuance or two that I'm ignoring -- one relates to which party has the claim against the drawee upon such a dishonor, and another is an ID question.)
That doesn't mean a bank who isn't the drawee must cash it. Such a bank (the depository bank) is at risk if one or both or the endorsements are forged. As a practical matter, though, if you are depositing such a check into the account of one of the two payees, especially if you do it through an ATM, it'll likely clear just fine. And if it doesn't, adding additional language on the back of the check wouldn't have helped anyway.
Disclaimer: I'm probably not licensed in your jurisdiction, and even if I am, this is general information and not reliable legal advice. Laws vary, and I haven't seen the check or your account agreement. See a lawyer licensed in your jurisdiction for advice you can rely on.