Question: This Shabbat (Vayakhel/Pekudei), the gabbai called up a levi for shvii, and as ba’al korei, I knew he was going to make a hosafa and give acharon/chazak to someone else. I quickly told him the levi cannot come up, but that they should switch the intended olim, having the levi wait for acharon. After laining, someone suggested we should have relied on the Sephardi minhag that kohanim and levi’im can have aliyot after the first three. Who was right?

Answer: The reason a levi gets the second aliya is to honor his status, which is lower than a kohen’s and higher than a yisrael’s (Gittin 59b). Once there is a hierarchy, giving a kohen or a levi a lower than prescribed aliya, especially giving an aliya after another "tribesmen" can give the impression that one of them is disqualified from his status (see ibid.).
All agree that the three aliyot during the week and the first three of Shabbat and Yom Tov morning are given to kohen, levi, and yisrael, in that order. According to Sephardi practice, starting with the fourth aliya, we can give aliyot to kohanim and/or levi’im, as long as it is not to two in a row and that when we call them, we announce "… even though he is a kohen" (Shulchan Aruch, Orach Chayim 135:10). The Rama (ad loc.) says that Ashkenazi minhag is that they cannot get aliyot until after the required seven. However, Ashkenazi minhag has changed somewhat: kohanim/levi’im do not get even hosafot except for maftir and acharon, but they can be even back-to-back (Mishna Berura 135:36, based on the Levush). On the side of leniency, even if acharon is one of the seven, the importance of its finishing the reading makes it appropriate for kohanim/levi’im (ibid.).
The Taz (OC 135:9) points out the "self-fulfilling prophecy" element of these matters. If the rule is that a certain aliya is appropriate for a kohen/levi, then receiving it cannot cast aspersions on them. This observation helps justify Sephardic leniency but makes it more difficult (while still possible) for Ashkenazim to rely upon the lenient opinions, when in the shul at hand, it is not an aliya that kohanim/levi’im receive. In your case, since the previous levi received an aliya long before, aspersions will not go back onto him (see Beit Yosef, OC 135). However, in general, we do not leave it up to the kohen/levi to decide if they are willing to put up with possible aspersions upon themselves.
On the other hand, Halacha does consider other factors in this matter, including the embarrassment of coming up for the aliya and not being able to receive it (see Mishna Berura 135:35). (It is not fully clear if the embarrassment begins in earnest from the time one’s name is called and he is thus expected to get up (see Berachot 55a), or only when he stands by the bima – see ibid. and Mor U’ketzia to OC 135). Yet, classical poskim do see your solution, of giving him a subsequent aliya, as a good remedy to embarrassment. The Shulchan Aruch (ibid. 6) says that if a yisrael was called for the first aliya due to absence of a kohen and then a kohen comes in before the yisrael begins the beracha, the yisrael waits at the bima until he can get the aliya. The Mishna Berura (ibid.) embraces that idea for our general case. So what you did was an excellent way to deal with the situation, and better than ignoring our minhag of not giving aliyot before acharon.

Bemare Habazak - Rabbis Questions (513)

Rabbi Daniel Mann

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There may have been other viable possibilities. Even if the yisrael was informed about his aliya, until he is called up, nothing firmly binds the shul to give him one. Of course, decency calls for keeping one’s word (see Bava Metzia 49a), but mistakes or changed circumstances can legitimize asking the yisrael to forgo his expected aliya and "compensating" him in the future. (Which idea was better might depend on a quick appraisal of who is likely to be insulted.) If it was important to give chazak to the yisrael, it was possible to give maftir to the levi (when it is fine to split the berachot and the haftara reading is a good question – see Rama, OC 284:4; Ishei Yisrael 38:56).