Can a cleric "multi class" between domains? [duplicate]

I have a player asking me if there is a mechanic that would allow them to take on a second domain, much in the same way a player can multi class. My gut here is no and I am contemplating instead finding out which 2 domains they wish to combine and then forming my own homebrew deity and domain that takes aspects of each, but not everything. But is there a RAW way that a player could take on multiple domains as a cleric?

pathfinder 1e – Lore help sought: how might my players change a deity’s domains?

The short setup: my players believe they’ve angered a major deity and want to atone for their actions. Since the deity in question is Desna, who wants to reclaim the Beasts domain from Lamashtu, one of the “obvious” options is to help her achieve that goal.

I’ve been looking for lore about how PCs (and mythic ones at that) might be able to even nudge the cosmic balance such that one deity might take a domain from another.

I know the ultimate answer is “whatever the GM says works works”. I’m hoping that there’s some obscure bit of lore that I’ve overlooked that might point in a helpful direction.

So: what, if any, precedent/lore/… is there in Golarion for mortals to change – or aid in a change to – a deity’s domains when there’s no chance of a negotiated transfer?

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complexity theory – A question about domains in Karp reductions

A basic question or request for clarification regarding Karp reducibility:

Let $Sigma^*$ be the set of all finite strings of 0’s and 1’s. Call a subset of $Sigma^*$ a language. Let $Pi$ denote the set of all functions from $Sigma^*$ into $Sigma^*$ that are computable in polynomial time. According to Karp, a language $L$ is reducible to a language $M$, also denoted $L leq_K M$, if there is a function $f in Pi$ such that $f(x) in M Leftrightarrow x in L$.

For many problems, however, we are interested in the difficulty of determining membership in subsets of domains other than $Sigma^*$. To address this, Karp briefly discusses encodings: Given a domain $D$, there is often a natural “one-one” encoding, $e: D rightarrow Sigma^*$. He then says that given a set $T subset D$, $T$ is recognizable in polynomial time if $e(T) in mathcal{P}$. But don’t we, in practice, typically consider $T$ to be recognizable in polynomial time if, for any $x in D$, we can determine whether $x in T$ in polynomial time? On the face of it, this doesn’t seem to be the same as Karp’s definition, since there is no guarantee that $e(D) = Sigma^*$.

Similarly, according to Karp, $T leq_K U$ where $T subset D$ and $U subset D’$ if $e(T) leq_K e'(U)$ where $e: D rightarrow Sigma^*$ and $e’: D’ rightarrow Sigma^*$. However, when we are actually proving $T leq_K U$ for some real $T$, $U$, $D$, and $D’$, don’t we frequently just define an $f: D rightarrow D’$ computable in polynomial time, confirm that $f(x) in D’$ for any $x in D$, and show that $f(x) in U Leftrightarrow x in T$ for any $x in D$? Again, this doesn’t seem to be the same thing as Karp’s definition if $e(D) neq Sigma^*$.

What am I missing?

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