There is NO criteria for EO. NONE.
Not absolutely correct. The normal take off weight limits cover WAT requirements for climb OEI.
However, when it comes to terrain clearance, you are correct .. it's up to the operator/pilot to make sure that the data has been acquired and the sums done to establish a suitable maximum weight for the day to ensure that, at the very least, the minimum terrain clearances for the net flight path are met.
The ONLY answer is that is varies very specifically by aircraft.
To some extent, the numbers will have some similarity for twins, triples, and quads as the WAT requirements vary with the number of engines.