Hey Joe, far be it for me to come close to Henry's excellent explanation, but I would also wonder if 'kasama' is acting like a pseudo-verb here (like gusto ko / kailangan ko / dapat ko). These pseudo verbs seem to act like a concept that is possessed by the speaker (for ko) e.g. 'Gusto ko ng pizza' is literally 'i have a like of pizza' or ' i have a yearning for pizza'. I think of them as pseudo verbs because they don't really modify into different tenses, and they aren't actions. So I think of your sentence as [kasama ][ko ][Kumakain ][ng tanhalian] ['in the company of][possessed by me][actor focus: was eating][object:lunch] [ang kapatid][ko ] [actor:sibling][of mine]

"Kasama kong kumakain ng tanghalian ang kapatid ko." = I eat/am eating lunch with my sibling. ? Maybe it's better to think of it as... (Together with me) (my sibling eats lunch) ? "Sino ang kasama mong kumakain ng tanghalian?" = Whom do you eat/are you eating lunch with? Is this translated like this?: (Who) (with you) (is eating lunch)? No need to break them down since you already got both of those conversions right. “Kasama” + “ko” = “with me”, + “mo” = “with you” (singular), + “niya” = “with him/her”, + “namin” = “with us”, + “ninyo” = you (plural), and “nila” = “with them”. “I am taking a walk with my dog” may be said, using “kasama”, in any of the following ways: 1. “Ako ay naglalakad kasama ang aking aso”. 2. “Naglalakad ako kasama ang aking aso”. 3. “Ang aso ko ay kasama ko na/kong naglalakad.” 4. “Kasama ko na/kong naglalakad ang aking aso.” So, it’s no. 4 above that is of the same structure as the one you were asking about. In "Sino ang kasama mong kumakain ng tanghalian?" though, “kasama mong” is not transmutable in any other way unless we modify the question to, “Pag kumakain ka ng tanghalian, sino ang kasama mo?” (When you eat lunch, who are you with?).