The 3rd Aliyah must be given to a Yisrael if there is one present (assuming that the first two went to Kohen and Levi). See Shulchan Aruch, 135:3. (Link at the bottom)
Subsequently on a day when more than 3 people are called up, the later aliyot can go to anyone but the normal minhag is to give them only to Yisraelim and to add extra ones on a Shabbat or Yom Tov if we want to call up more kohanim or leviim. (Appears from the ou.org site that Ashkenazim are more strict on giving them to Yisraelim, other than acharon or maftir, Sefardim are more flexible)
The best source I have is Orach Chayim Chapter 8:
On Mondays, Thursdays, and Sabbath afternoons the Torah is read, starting just after the portion that was read on that Sabbath morning (135:1-2). This reading is divided into three parts; but more parts may be added if a religious celebration is taking place (135:1). These parts are read by a KOHEN, a Levite, and an Israelite (135:3). On exceptions to this order, for example if no KOHEN is present or able to read, see 135:4-13. On Sabbaths and holidays, when additional parts are read, see 135:4,10;136:1; 141:6 on the persons who read them. The reading must be at least nine or ten consecutive (see 144:1-2) verses long (see 137:1), and each person must read at least three verses (137:2); on errors see 137:3-6. Each person's reading should start and end with a good topic, and should not start or end only one or two verses away from a paragraph; see 138:1.
ou.org also mentions it here:
Concerned that the order of aliyot could lead to dissension, Chazal
established a standardized sequence for aliyot whereby the first
aliyah is always given to a Kohen, the second to a Levi and all
subsequent aliyot to Yisraelim (Mishnah Gittin 5:8; SA, OC 135:3).
Assuming there are sufficient Yisraelim in shul, the current
Ashkenazic practice is to not give a Kohen or Levi any of the later
aliyot except for Maftir, or, if additional aliyot are added on
Shabbat, the very last one known as “achron” (MB 135:24, 36-37).5
Sepharadic practice is to give a Kohen or Levi subsequent aliyot as
well (SA, OC 135:10; Yalkut Yosef 135:31).
For a straight translation of the chapters see: