advise, agree, demand, insist, prefer, propose, recommend, request, suggest, urge etc.

Geoffrey: I think you should visit a specialist.
Geoffrey advised that I should visit a specialist.

Susan: Yes, Harry, you are right. You’d better accept that offer.
Susan agreed that Harry should accept that offer.

Customer: I want you to give me a full refund!
The customer demanded that the company should give him a full refund.

Geoffrey: You really must try the new Opel.
Geoffrey insisted that I should try the new Opel.

Howard: I’d rather you came to my party, Susan, and not to Julie’s.
Howard preferred that Susan should go to his party.

Jill: What about going to the sauna tonight?
Jill proposed that they should go to the sauna.

Jill: What about going to the sauna tonight?
Jill recommended that they should go to the sauna.

Employees: Could we have the staff meeting on Tuesday instead, Boss?
The employees requested that the staff meeting should be on Tuesday.

Jill: What about going to the sauna tonight?
Jill suggested that they should go to the sauna.

Secretary to the President: Now, it’s really high time that you handed in your resignation, Sir.
The secretary urged that the president should hand in his resignation.

Reporting verb + THAT-clause
Common reporting verbs Reporting verb + THAT-clause with subjunctive