The sure sign of a lawyer who was soundly, but not sufficiently, beaten as a clerk.

I shan't give it to you William until the following day.

The “next following” day is a redundancy that speaks to that nervousness that the day you have in mind — namely, the one immediately after the one you’re thinking about — might not be the one your adversary does. For a day “following” this one might, conceivably, fall some indeterminate time — four days, eight days, who knows, even three hundred and fifty-seven days? — in the future. All days after this one “follow” this one; unless you say the “next following” day, cannot be sure it will be the one tomorrow.

This is the kind of argument you'd expect from that posh ginger girl on Just William. Allow me to channel my inner Richmal Crompton:

“Violet-Elizabeth, give me my rubber back.”
“I shan’t.”
“But you said you would.”
“I most thertainly did not.”
“You said you’d give it to me on the following day.”
“Tho I did. But not this following day. Another one. In Theptember, I shouldn't be thurprised.”

It pains me, readers, to think an adult learned in the ways of the law could be vexed by such a thought.

Firstly, a following business day is not the same thing as the following business day. That definite article restricts you to a single day.

If you encounter such a fellow, and wish to engage on the argument — if you can resist the temptation to administer a restorative beating — you can always use the word “next”.

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