English equivalent of the Greek “When Muhammad does not go to the mountain…”?

Question

In Greek, there is an expression which translates literally to

When Muhammad does not go to the mountain, the mountain goes to Muhammad.

The expression is used when the speaker believes that they can approach something which cannot approach them. Essentially, the speaker wants to say that if something does not happen one way, it will happen the other.

For example, someone who goes to see their friend who could not accept an invitation to come over might say on arriving, “When Muhammad does not go to the mountain, the mountain goes to Muhammad.” The intended meaning is “Since you couldn’t come over, I came instead.”

Usually, this idiom is translated to a similar-sounding one in English, but as I explain below, the meaning is different.

My Research

There are expressions involving Muhammad and a mountain in several language. In most of them, it seems that the meaning is the same as the one in English.

The English expression is

If the mountain won’t come to Muhammad, then Muhammad must go to the mountain.

The meaning, according to The Free Dictionary, is

If one can’t have one’s way, one must give in.

While the meaning seems close, it is quite different. The English idiom implies that the second alterative is worse than the first, in the sense that, if the mountain wouldn’t go to Muhammad, he would have to go there himself.

However, the Greek idiom switches up the subject and object in the sentence (“When Muhammad does not go to the mountain…”). There is no implication that the second alternative is worse than the first. The focus, as I said before, is on the fact that if something is to happen, it can happen in whatever way it has to.

Answer 1

Consider this a partial answer, since it fits your example but is less versatile than the original expression. I have heard this cliche used multiple times, and the full version goes something like this:

If you can't come to the party, we'll bring the party to you.

This basically means that if someone can't go out, nonetheless the event can be brought to the person. The latter part by itself has been used in catering ads (obviously) but also to refer to an in-house visit like the one you mention in your example (Jenna Bayley-Burke, Compromising Positions):

"Plan B. We bring the party to you," Sophie said, settling in beside Daphne for an afternoon of soap operas and girl talk.

Other samples include the if-statement as a setup, like this one from Russell Banks, The Angel on the Roof:

The man needs company, he needs to feel wanted, and especially he needs to feel needed. We ought to make an excuse to have a party, a Valentine's Day party, say, and march out there and say to him, "Merle, if you won't come to our party, then we'll bring the party to you!"

Or this one from Bob and Karen Freitas, Our Journey from Brokenness to Blessing:

"If he can't come to the party," one person said, "we'll bring the party to him!"

Finally, it can be used in extended uses, like when the villains refer to a fight as a party (Trenten Lee Stewart, The Mysterious Benedict Society and the Riddle of Ages):

"I'm afraid she's a party pooper, gentlemen," McCracken said. "Simply isn't in the mood today. Very well, my dear! We'll bring the party to you! You'll notice I'm not offering you a chance to surrender. No, you had best use your darts wisely, for we do mean you harm. Did you hear me clearly, Kate? We mean you harm."

Answer 2

one way or the other has a neutral sense:

which of two possibilities will be chosen:

They've had two weeks to think about it, and now they have to decide one way or the other.

As for your intended use in

“Since you couldn’t come over, I came instead.” That is, one way or the other, we were able to meet.

Answer 3

The English equivalent is almost identical to the Greek one. It is

If Muhammed won't go to the mountain then the mountain must go to Muhammed".

I've known that for seventy years and I've never heard the reversed one that you claim is the English version. However I'm British, perhaps the reversed one is American.