Malbim Ayelet HaShachar Klal 352
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הכפרה בעד אחרים כתוב אחריו שימוש מלת "עליו", והכפרה בעד עצמו כתוב אחריו שימוש מלת "בעד" – "וכפר בעדו". (ויקרא סימן לג)
Ayelet Hashachar, translated by Betzalel Avraham Feinstein, 2021
Whenever atonement is for the sake of others, the word עליו (upon it) is written afterwards, and whenever atonement is for the sake of oneself, the word בעד – as in וכפר בעדו (shall make atonement for himself)⁶³⁷ - is written afterwards.
footnotes: ⁶³⁷ Leviticus 16:11.