This is a very good question. I do not have a comprehensive answer. I still try to give an answer, hoping I can shed some light on the grammatical structure. I hope someone more knowledgeable can give you a better answer.
Das ist etwas, das anders hätte gemacht werden können.
das anders hätte gemacht werden können. is a relative clause, specifying etwas. Your confusion might stem from the fact, that there is the rule:
In a relative clause the finite verb is in last position.
And the finite verb is actually hätte! We can verify this, when we use the phrase in a main clause:
Etwas hätte anders gemacht werden können.
In the main clause, the finite verb is in second position, and we happily find hätte in second position here, and the complex verbal phrase is split by anders, so this is verifying that hätte is indeed the finite verb here.
So our finite-verb-in-last-position-in-subordinate-clause rule is violated here. This is, because this complex verbal phrase with a modal in perfect is an exception of the rule. Unfortunately, I do not know why this is the case. So, all I can give you is to explain the details of the grammatical structure here and tell you that this structure is an exception. (Since I cannot tell a more general rule which makes this exception appear a more systemically fit, I consider my answer incomplete.)
So let's look at this complex verbal phrase hätte gemacht werden können: This is a passive construction (etwas wird gemacht) combined with a modal verb (etwas kann gemacht werden), which is in Perfekt tense (etwas hat gemacht werden können) and on top it is also Konjunktiv mood (etwas hätte gemacht werden können).
Let me summarize the relevant exception rules here:
In a comment, Satish Vasan has mentioned this very good resource (in German) with an overview over the exceptions.