I'm not able to take the time for an extensive search for data on "two or more victims" homicides right now, but I'll definitely look when I can. It's a bit difficult, as mass shootings have previously been defined differently by the FBI and other record-keeping entities. I'll have to go through the data to find 2- and 3-victim homicides and then see if I can filter them by type of murder weapon to get a figure for those committed with guns.
Under the former standard definition of "mass shooting" (four or more victims), the total number of incidents since 1970 is quite small, although the rate of incidents has increased over the last 15 years. There's a comprehensive study of the more recent mass shootings by the Congressional Research Service that makes this clear: org/sgp/crs/misc/R44126.pdf
A recent USA Today article noted that there have been c. 900 fatal mass shooting victims in the past seven years. That's c. 900 against approximately total 70,000-80,000 firearms homicides over the same time period. I suppose it's possible that gun murders with 2 or 3 victims would constitute a significant portion of that total...but it strikes me as unlikely in the extreme.
Moreover, I don't think the re-classification of those crimes as "mass shootings" is particularly valid, as it lumps together crimes with very, very different motivations, different perpetrator characteristics, choices of murder weapon, etc. It makes for a good soundbite, but is less useful for analysis and for informing future policy.