Yes, but not because of any disagreement with the living will’s contents. Instead, a living will may be contested by a formal objection against the document’s overall validity. In other words, you must contest the will by claiming that it’s not a valid document in the first place.
You can do this in several ways. For instance, most states require that a living will include:
A signature, a notary public’s signature, and perhaps the signature of one witness (sometimes, two witnesses)
Signatures from adults of sound mind and body
That the person the living will pertains to is not pregnant (or does not know they are pregnant)
That the attending physician was notified of the will
If any of these clauses are broken, you may have cause to contest a living will. Suppose a successful case for contesting is made. In that case, doctors will usually withhold final decisions if possible but will often default to attempting to keep the affected person alive until another decision is made.