(1) *I'm buying it whether I can afford it.
(2) I'm buying it whether I can afford it or not.
(3) I'm buying it whether I can afford it, or whether I have to take out a loan.
I think (1) doesn't work, because it doesn't contain an or-coordination, as in (2), which works fine.
How about (3)?
Can the or-coordination reside outside the whether-clause, as in (3)?
I wouldn't use (3) myself; I would say (4) instead:
(4) I'm buying it whether I can afford it or (I) have to take out a loan.
(This doesn't mean that I don't think (3) works. All it means is that I'm not too familiar with constructions like (3), if it does work.)
But I've seen constructions similar to (3). So I'd like to know whether constructions like (3) are well formed.
Research I've done
I've looked up a few grammar books including CGEL by Pullum, but to no avail.
Specifically, I'd like to know how common constructions like (3) are compared to its counterpart like (4), and whether the former is a well-formed alternant of the latter simply when the whether-clause is too long and/or complicated to be written in a single clause.
Further clarification and an attested example
The question is not about the general use of 'whether', but only about the use of 'whether' in an exhaustive conditional construction where the whether-clause is functioning as an adjunct of the matrix clause.
At the time of this writing, I've received two answers, both of which claim that (3) doesn't work. But I've just found an example similar to (3):
(5) And I want to assure you that this President is going to continue to work with members of Congress, like Congressman Andy Harris, to make sure that you have the resources and the support that you need to accomplish your mission — whether that be saving people from human trafficking, whether it be sparing families the scourge of narcotics, drug abuse, addiction, and overdose, or whether it be stopping the violence of MS-13 and other gangs that are flowing into our country.
The difference between (3) and (5) is that (5) has a more complex construction of 'whether A, whether B, or whether C', and that the verb be in (5) is in the present subjunctive form.
Hopefully final edit
In response to the claim that the whether-clauses in (5) are not mutually exclusive, here's another example from "Remarks by Vice President Pence in Press Gaggle":
(5') So, we’ll — all these steps are designed to demonstrate this is a President who embraces his role as leader of the free world. But with regard to Venezuela — whether it be Russia or whether it be Iran — the President’s message is very clear: Russia and Iran have no business in Venezuela. They should step aside and allow the people of Venezuela to restore their democracy and their freedom.
I'm sure 'it being Russia' and 'it being Iran' are mutually exclusive.