(b) Airplane category rating with a single-engine class rating. A person applying for an airline transport certificate with an airplane category and single-engine class rating who holds an airline transport pilot certificate with another aircraft category rating must:
Please note that the above quoted regulation applies specifically to a person who holds an ATP in
another category
other than airplane. As the holder of ATP with multi-engine class rating in the airplane category, Phil Squares need not take the knowledge test to qualify for the addition of a SEL class rating to his Airplane, MEL ATP. Further down in FAR 61.165 is paragraph (e) which describes the requirements to add SEL class rating to an airplane category ATP:
(e) Additional class rating within the same aircraft category. A person applying for an airline transport certificate with an additional class rating who holds an airline transport certificate in the same aircfaft category must—
(1) Meet the eligibility requirements of §61.153, except paragraph (f) of that section;
(2) Comply with the requirements in §61.157(b) of this part, if applicable;
(3) Meet the applicable aeronautical experience requirements of subpart G of this part; and
(4) Pass a practical test on the areas of operation of §61.157(e) appropriate to the aircraft rating sought.
Note that there is no requirement to receive an endorsement or any specific training to qualify for the addition of a class rating to the ATP.
61.39 states in part:
(c) A person is not required to comply with the provisions of paragraph (a)(6) of this section if that person:
(1) Holds a foreign-pilot license issued by a contracting State to the Convention on International Civil Aviation that authorizes at least the pilot privileges of the airman certificate sought;
(2) Is applying for a type rating only, or a class rating with an associated type rating; or
(3) Is applying for an airline transport pilot certificate or an additional rating to an airline transport pilot certificate in an aircraft that does not require an aircraft type rating practical test.
Note: Para (a)6 is the one that requires an endorsement. Does not apply in this case.
So just train to proficiency in a SEL airplane and complete an 8710. The ATP PTS contains a matrix which stipulates the required Areas of operation that apply. This can be used as an outline for your test preparation. Confer with a local DPE to verify the correctness of what I have stated here and arrange to take your ATP SEL checkride. Good luck!
Best regards,
Westhawk