Did some research on your list (not all of them, but mostly the 'not reported' ones), and found some updates.
Numbers may be off as order of list was changed a few times.
4) Before 24 January 2021 West Whiteland PA, 4* killed (not reported)
Deaths were gunshots
https://www.nbcphiladelphia.com/new...d-following-suspected-murder-suicide/2678504/
6) 31 January 2021 Sand Springs OK, 4* killed (not reported)
Deaths were stabbing (killer used knife on himself as well)
https://tulsaworld.com/news/local/c...cle_6909bbf6-64a2-11eb-8741-1f89d8c600f4.html
9) 18 February 2021, Fayette TN, 4* killed (not reported)
Edit: #10
Deaths were gunshots
https://www.actionnews5.com/2021/02/23/unanswered-questions-remain-after-four-death-murder-suicide/
12) before 5 March 2021 Grants? NM, 4 killed (not reported)
Edit: #13
Not one incident.
The four bodies were found at same time, but three were killed over a week's time, then fourth death a month later.
https://www.koat.com/article/sunport-quadruple-murder-suspect-sean-lannon/37466607#
13) 14? March 2021 Indianapolis IN, 4 killed (not reported)
Edit: #14
Deaths were gunshots
https://fox59.com/news/indycrime/prosecutor-to-give-update-on-weekends-quadruple-homicide/
30) 10 May 2021 Chesterfield County VA, 6* (negligent homicide, smoking in bed)
If you are going to include accidents like this, how about carbon monoxide poisoning? Family of 7 dead from carbon monoxide poisoning. Make a difference if it came from the vehicle in garage or from a faulty furnace? (not known right now which was the cause)
https://globalnews.ca/news/8469817/minnesota-family-deaths-carbon-monoxide-poisoning/
33) 2 June 2021 Fort Wayne IN, 4 killed (not reported)
Edit: #35
Deaths were stabbing, mother was strangled and stabbed
https://www.wane.com/news/crime/arm...s-police-investigate-problem-at-se-side-home/
Case 39?
There were 37, then you added a new #32 (so that would be 38 total), then jumped to #40?
58) 10 October 2021 York County SC 4 killed (vehicular homicide)
58) 29 November 2021, Bay Country FL, 4* killed (reckless driving)
Two #58s?
60) 30 October 2021 El Paso County CO, 4* killed (not reported)
Can't find official confirmation, but killer was owner of gun shop....
60) before 18 November 2021 Washington County MD, 4* killed (multiple)
Two #60s?
One not on your list (found when looking for June incident in Fort Wayne).
November 29, 2021 Fort Wayne, IN 4 killed (shot)
https://www.fortwaynesnbc.com/2021/11/30/family-members-identified-murder-suicide-monday-night/