Go off vs go on?

In comments, John Lawler wrote:

Really common verbs like go, come, have, do, look, hear, take, give, bring, get, seem, and some others (note how short they are) are likely to be used in idioms. One of the most common kinds of idiom is phrasal verbs, which use really common prepositions like off, on, up, down, over, under, out, in, and some others, almost always idiomatically. Combining these two idiom chunks -- come/go plus off/on leads to any number of idiomatic senses, all of which have to be learned individually. That's the problem with idioms.

And:

The solution is to get a dictionary of phrasal verbs with examples in context. One-word glosses are not useful except as placeholders.

There are subtleties involved with the use of the multi-word verb 'go off' in the intransitive sense of 'occur'.

Cambridge English Dictionary lists this sense:

go off {phrasal verb} [less ambiguously, multi-word verb]

...

{happen}: to happen in a particular way:

• The protest march went off peacefully.

Merriam-Webster shows that the usage is not purely British, and refines the definition:

go off {intransitive verb}

...

5: to follow the expected or desired course : PROCEED

• the party went off well

A complication here is that replacement by 'took place' can occur in the CED example:

• The protest march went off peacefully. ⇔ The protest march took place peacefully.

But not in the M-W example:

• The party went off well. ⇔ *The party took place well.

It is probable that 'go off', having the implications of 'in a particular way', licenses 'well' whereas unmarked 'occur', 'happen' and 'take place' don't. Note that M-W is over-prescriptive here, as '... the rally went off rather badly' is totally idiomatic, at least in the UK.

Going further, it seems that 'go off' in this sense requires or at least is almost always accompanied by an (evaluative) adverbial.

• The event went off rather well, don't you think?
• It all went off beautifully / like a dream.
• Let's hope it all goes off without a hitch.
• ??It should go off later today.
• *Have the finals gone off yet?

....................

Similarly, 'go on' and 'happen', while being fairly close synonyms, are not fully interchangeable:

• What is going on here? ⇔ What is happening here?
• There's a lot going on at the moment. ⇔ There's a lot happening at the moment.
• He's a lot going on at the moment. ⇔ ??He's a lot happening at the moment.
• *What do you think will go on next? ⇔ What do you think will happen next?

The nominalisation 'goings on' carries a strong flavour of human or at least sentient involvement, and this is in some degree common to the verbal usages. The last example, being pretty unmarked for this, needs 'happen' or in a formal register 'occur'.