On a day that you call up 3 alios, read no less than 10 pesukim except for the 9-possuk Parshas Amalek on Purim. (ShA1)
A minhag has spread to split the first aliyah of the upcoming Parsha into three for the kria of Shabbos Mincha, Mondays, and Thursdays as printed in the siddurim. This practice is not m’akayv. (MB 4)
In the following 2 cases (only) you will have to go back and read skipped pesukim (or even 1 word):
The weekly Shabbos morning portion.
When a second sefer Torah is read for the obligation of the day and the skipped piece was crucial to the topic of the day. (ShA 3 – MB 8,11)
In the above cases, make a new aliya from the beginning of the skipped possuk plus an additional two pesukim. The oleh should say the berachos before and after. (MB 8,9)
Make a new aliya even if the tzibbur already daavened Musaf before realizing their mistake. (ShA 3)
If a possuk was skipped in the seventh aliya and it was caught before Maftir, do not make a new aliya. Instead, have the Maftir begin his repetition from the skipped possuk until the end of the parsha. (MB 10)
L’chatchila, do not repeat pesukim already read by earlier olim even if you plan on adding 3 new pesukim. An exception: the paray hachag from Chol HaMoed Sukkos. (ShA 6 – MB 19,25)