Given an algorithm, is it possible to find all other equivalent algorithms for the same computable function in the same model For any computable-function, there may be multiple different algorithms (possibly countably infinite). For example, sort has many different implementations/algorithms, that we know of or that we have found so far. They all produce the same output for the same input.
Given any specific computable-function or even a specific instance of an algorithm/implementation (for any model of computation, functional in lambda calculus, imperative in turing machines, or any other) for it, is it possible to enumerate/find all other equivalent algorithms/implementations for that same computable-function, for the same model.
ie. If I have an algorithm or even a specification for sort, it is possible to find the other algorithms for sort?
Interpreting your problem as finding a computable $f$ such that $f\big(\langle M\rangle\big)=\langle M'\rangle$ with the property that $M'$ enumerates all programs equivalent to $M$, i.e. all $M''$ with $L(M'')=L(M)$, the answer is no (such $f$ does not exist).
One way to show this is to observe that such $f$ would place the language $\left\{\big(\langle M_1\rangle, \langle M_2\rangle\big) \big| \; L(M_1)=L(M_2)\right\}$ in $RE$, while it is known that this language is $\Pi_2$ complete and thus not in $RE$. You could formulate this relative to any admissible numbering, and not necessarily in the language of Turing machines.