A few days ago I discovered baptisms from Our Lady of Sorrows (Sorrows) recorded in a register from Assumption of the Blessed Virgin Mary (Assumption). It isn’t a wildly important find, but it’s worth mentioning.
The Assumption register begins with an alphabetical index to baptisms 1881-1888.  Following that, there are three more pages of index entries with a heading that reads "Baptizatorum In Ecclesia St. M. Dolorosae 1406 W. Jackson from 3d January 1875 to 26 July 1889."  This second index covers 111 Sorrows baptisms that were recorded on pages 201 to 228 of the Assumption register. 
I haven’t compared all of the entries in the Assumption register with entries in the Sorrows register, but a quick check suggests the Assumption register contains a small subset of baptisms that are also in the Our Lady of Sorrows register. For example, the Assumption register has a single entry for 12 September 1875--the baptism of Rosam Antiquo.  The Sorrows register has four entries for that date, including the Antiquo baptism. 
So, how did this duplication of entries come to be and what does it mean? In short, I don’t know. I’m tempted to take a close look at the information and handwriting in records from the two parishes to try to puzzle out something about the who, what, when, where, and whys of this discovery but it would have no bearing on my current research project, so I can’t afford the time.
I can offer a few suggestions, though, based on what I’ve learned:
1) If you find an early baptism in a Sorrows register, check to see if there’s a matching entry in the Assumption register. There might be small, but potentially useful, differences. For example, in one case, a marriage is noted in the margin of an entry in the Assumption register but not in the Sorrows register.
2) If you don’t find a baptism in a Sorrows register, it might be worth checking the Assumption register. There’s a small possibility there’s something recorded at Assumption that wasn’t recorded at Sorrows.
3) Both Sorrows and Assumption were founded in 1874 as missions for Chicago’s Italian community and both congregations originally met in the basement of St. Patrick’s Church.  Clearly the histories are connected and that’s likely how the baptismal records of one came to be recorded in the register of the other.
4) Sorrows is listed as an Italian parish in the Bochar book, but there are many Irish-surname baptisms recorded in the early register, perhaps, in part, because of the association with St. Patrick’s. Sorrows should be on the list when searching for hard-to-find Irish baptisms.
5) I suspect the entries in the Assumption register were copied from another source; I think it's more likely the entries in the Sorrows register are original.
Here's an easy way to find the Chicago Catholic records on FamilySearch:
Use https://www.familysearch.org/ark:/61903/3:1:S3HY-XCRC-8MX?owc=waypoints&cc=1452409 to go to the list of parishes.
And, from there, just click a parish name to see what records are available.
Just one thing that's important to know: This approach bypasses the catalog entries which may have important additional information. For example, the link to the Assumption baptismal register is titled "Baptisms 1881-1888" giving no indication that there earlier records from Sorrows are included. The catalog entry hints that there is more: "Item 3: baptisms, 1881-1888 (includes 2nd index: 1875-1889)."
 "Illinois, Chicago, Catholic Church Records, 1833-1925," FamilySearch (https://www.familysearch.org/ark:/61903/3:1:S3HT-6RQS-NFN) > Assumption BVM Parish (Chicago: Illinois St) > Baptisms 1881-1888 > images 1-13, Assumption of the Blessed Virgin Mary (Illinois St), baptismal register, 1881-1888, n.p. [first twenty-six tabbed index pages]..
 Ibid., images 14-15, Assumption of the Blessed Virgin Mary (Illinois St), baptismal register, 1881-1888, n.p. [three pages preceding p. 1].
 Ibid., images 115-129, Assumption of the Blessed Virgin Mary (Illinois St), baptismal register, 1881-1888, 201-228.
 Ibid., image 116, Assumption of the Blessed Virgin Mary (Illinois St), baptismal register, 1881-1888, 202, Rosam Antiquo, 12 September 1875.
 "Illinois, Chicago, Catholic Church Records, 1833-1925," FamilySearch (https://www.familysearch.org/ark:/61903/3:1:S3HT-6RQS-NFN) > Our Lady of Sorrows Basilica (Chicago: Jackson Blvd) > Baptisms 1874-1894 > images 31-32, Our Lady of Sorrows Basilica, baptismal register, 1881-1888, 39-40.
 Jack Bochar, Locations of Chicago Roman Catholic Churches 1850-1990, 2nd ed. (Sugar Grove, Illinois: The Czech & Slovak American Genealogy Society of Illinois, 1997), 13, 23; pdf, "Genealogy Resources," Archdiocese of Chicago (https://archives.archchicago.org/documents/1004501/1006367 : accessed 7 August 2019)