Brachylog, 10 bytes
=ᵍbᵐbᵐlᵍ=l Explanation
=ᵍ Group all equal elements together bᵐbᵐ Remove the first element of each group twice. This fails if there are fewer than 2 elements lᵍ Group elements together that have the same length = Are all elements of that list equal.? This only succeeds if the list has one element l Length. This will always succeed