O parágrafo apropriado da Parte 61 do CFR 14 é 61,63 (ênfase minha, a parte ' a menos que ' não se aplica no seu caso):
(c) Additional aircraft class rating. A person who applies for an additional class rating on a pilot certificate:
(1) Must have a logbook or training record endorsement from an authorized instructor attesting that the person was found competent in the appropriate aeronautical knowledge areas and proficient in the appropriate areas of operation.
(2) Must pass the practical test.
(3) Need not meet the specified training time requirements prescribed by this part that apply to the pilot certificate for the aircraft class rating sought; unless, the person only holds a lighter-than-air category rating with a balloon class rating and is seeking an airship class rating, then that person must receive the specified training time requirements and possess the appropriate aeronautical experience.
(4) Need not take an additional knowledge test, provided the applicant holds an airplane, rotorcraft, powered-lift, weight-shift-control aircraft, powered parachute, or airship rating at that pilot certificate level.
Então, para responder a sua pergunta, não, você não precisa de um cross-country, você não precisa de tempo sozinho em um avião multi-motor. Tudo que você precisa é um sinal de seu instrutor.