What differences do we have in sentences below expressing the same mood and the same sense using different ways to express the same things by using different grammar:

  1. She demanded him to buy that book.
  2. She demanded that he should buy that.
  3. She demanded he buy that book.
  • (3) is grammatical, though (3a) She demanded that he buy that book would be better. (2) is bad because of the mismatch between strong demand and weak should; again, (3a) is better, since the modal is already present in demand, which means, roughly, (say (must VP). And (1) is simply ungrammatical; demand does not take an indirect object with the Dative alternation. – John Lawler May 12 '18 at 0:29

The complement of demand is that which the demand requires.

She demanded {something}.

The {something} can be a tangible thing:

She demanded a better seat, one without a column blocking her view of the stage.

She demanded money.

The {something} can also be an action that someone must perform.

When the demand is not a thing, such as a better seat, or money, but an action which is to be carried out by another person, that action is expressed by a clause, and the verb can be marked as not being in the indicative mood but in the subjunctive:

The judge demanded that he pay a fine of $100.

There is also the pattern to demand {something} of someone.

What was demanded of them?

That sentence means, What were they required to do?

The prepositional phrase of {someone} is required. Putting the {someone} in an objective declension (him, them, me, etc) and omitting the preposition is not an idiomatic way to refer to the {someone} who must obey the demand.

The judge demanded of him that he pay a fine of $5000 and forfeit his driver's license for one year.

In contemporary English should normally expresses a strong recommendation or an urging, and therefore (to my American ear at least) it does not partner well with demand, which expresses a command, an order, a requirement that must be obeyed.

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