[Grammar] How do you propose we should do it?

'How do you propose we should do it.'
Is the above sentence correct? I feel like it's correct but at the same time I also feel like it's incorrect.

Piscean said:

It's OK in the right context. What makes you think it might be incorrect?

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Probably my grammar paranoia.

How do you propose we do it?

I thought propose should not be followed by should.

I always find the use of "should" after "suggest" and "propose" very grating. A couple of grammar sites say that it's used particularly in BrE but I don't use it.

How do you propose we do it?
What do you suggest I do?

emsr2d2 said:

I always find the use of "should" after "suggest" and "propose" very grating. A couple of grammar sites say that it's used particularly in BrE but I don't use it.

How do you propose we do it?
What do you suggest I do?

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I'm not a fan of should in this context but I think it's okay.

I'm with emsr2d2 on this one. I think it's wrong, regardless of common usage. propose clashes with should.

When you propose something to someone, you are suggesting an idea. It is up to the receiver to accept and adopt it.
But when you tell somebody that they should do something, you are giving an advice.
I don't see how the two can be combined. It is grammatical but not logical.

Piscean said:

Whether we like it or not, 'should' is sometimes used in English as an alternative to a subjunctive form. There is no 'clash'.

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Ah, I see. The use of should here is not the same as in How do you think we should do it? Is that right?