How much must be eaten from the lechem mishneh

Question

Inspired by following 2 questions:

Not eating from the Lechem Mishnah

Challah Loaves on Shabbat have a minimum size?

When eating a Shabbos Seudah how much must the ones that are being yotzee from the Bal Bayis in lechem mishneh and the bracha of ha'motzei eat from the challas themselves? Must they eat a cazayis of the lechem mishneh then may eat from whatever other bread they want (that wasn't part of the lechem mishneh) or may they eat even a little bit from the lechem mishneh and the rest from other bread? I have heard in the past their is a maklokes in this. Please post sources.

Answer 1

See the answer to the question "How Much Does One Need to Eat From the Lechem Mishneh?" here. To quote the conclusion:

The question is on Shabbat, where everyone must be connected to the lechem mishneh and wait to receive a piece (ibid.). We find that on Shabbat it is best to cut off a big enough piece in the beginning to suffice for the whole meal (ibid. 274:2). However, there does not seem to be a requirement for individuals to eat specifically a k’zayit from the lechem mishneh. (A person should eat a k’zayit of bread for it to be a meal and recite Birkat Hamazon and a k’beitza to justify the beracha on netilat yadayim.) However, being connected to the lechem mishneh and the beracha made on it can be accomplished with eating any quantity (Igrot Moshe, OC V, 16; Teshuvot V’hanhagot II, 171). This being said, there are sources that indicate that a piece less than a half of a k’zayit is not considered significant (see Eliya Rabba 174:2) and that one should show respect to the bread to which the mitzva is related (see Levush, OC 174:14). Therefore, people would do well to eat a half of a k’zayit (without exaggerating the size of k’zayit as many of us do on Pesach) from the lechem mishneh. However, one who dislikes the challa the host used for lechem mishneh or has health concerns with it can follow the basic halacha that he can go on to other bread after a small taste from the lechem mishneh. Similarly, hosts who make Hamotzi on a loaf that may not provide a k’zayit or even a half for all (e.g., with large groups or for those who use rolls or matza for lechem mishneh at seuda shlishit and then serve sliced bread or leftovers) need not feel guilty. One who is careful to provide a k’zayit to each guest from the lechem mishneh is praiseworthy (see Shemirat Shabbat K’hilchata 55:24 and footnote 15).

Answer 2

Shemiras Shabbos K'Hilchoso (52:15) writes that essentially they do not need to eat at all from the Lechem Mishneh, as the host making a blessing and eating from the Lechem Mishneh is sufficient, however because of "Chibuv Mitzvah", it is best that they should eat from the Lechem Mishneh, however that only requires a minimal amount, even less than a K'zayis.

However, it seems that R' Moshe Feinstein (quoted by the Shemiras Shabbos K'Hilchoso, ibid.) held that they are all required to eat a K'zayis.

(Source)