We don't replace a verb with DO when it follows a modal?

I say:

I can eat more than you can eat.
I can eat more than you can.
I can eat more than you can do.
I can eat more than you.

I can run faster than you can run.
I can run faster than you can.
I can run faster than you can do.
I can run faster than you.

Are all of them acceptable? If not, could you tell me the reasons?

User Piscean says:

The third in each group is not correct. We don't replace a verb with DO when it follows a modal.

But I see this:

do
auxiliary verb
used instead of repeating a verb that has already been used

'Will Kay come?' 'She may do.'
https://www.ldoceonline.com/dictionary/do

Is a contradiction between this sentence and what Piscean said (We don't replace a verb with DO when it follows a modal)?

User Piscean replies:
Yes. I should have qualified my statement more.
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So I am confused. I don't know whether we can replace a verb with DO when it follows a modal.

Could you help me, please?

The question was posted on https://goo.gl/2Q1ny1
(Why do I post the same question here? Because I don't get an answer.)