.

For electric railway fans the goal might be to ride every electric suburban, rapid transit, light rail, heritage streetcar and trolley museum in North America. Since most railway/trolley museums run on weekends and the ones in the northern climates are often closed in the winter, this would take some planning.
With steam engines, some only run one or two weekends a month, but theme parks run 5 to 7 days a week. Some, such as Santa Fe 3751, run "sporadically", although in recent years, there have usually been trips in either April or June.

I'm sure some of the years when the big steam fests like the TrainFestivals were held help to make for a "Big Year." But even this year, with only one big steam safari on my schedule, I was able to snag photos of 12 steaming engines since January. Would it make me a braggart to name them all?

If we are going for sheer variety, you could plan around "event" weekends such as the steam ups at the B&O Museum, and add to it with a visit to maybe Western Maryland Scenic or Wilmington & Western, who reliably offer steam operations. Another way to build your number count is to plan around a time when a railroad is bringing one steam engine into service while another isn't ready yet for a big inspection. That would lead to a double header weekend, sometimes seen on the Valley Railroad, or a seasonal change at the Strasburg RR.
A third way is to catch steam on the way to other steam. When the TrainFestival was in Rock Island, IL, a few people I know chose to stop at Abilene, KS to shoot AT&SF 3415 on the way home since it might be their only chance to see it, or be in that end of the country.
I will have to consult my photo files to see which was my Biggest Year.

As a proponent of epic road trips, I've managed to squeeze a few in this year, including two "bucket list" engines, the 844 and 3751. Leaving off engines built FOR amusement parks, lets see:

CN 3254, Scranton (though that could be considered cheating, since it goes by my tower)
ATSF 3751 in AZ & CA
GCRY 4960, Williams, AZ
Ventura County 2, Perris, CA
Rio Grande Southern 41, Buena park, CA
Disneyland 3, Anaheim, CA
Cedar Point 44, Sandusky, OH
Cedar Point 22, Sandusky, OH
UP 844, Denver, CO
West Side #9, Georgetown, CO
SLRG 18, Alamosa, CO
Six Flags 2, Arlington, TX
Silver Dollar City 76, Branson, MO
White Pass 70, Pigeon Forge, TN
White Pass 192, Pigeon Forge, TN

My "biggest year" was probably 2011:

SP 4449 (another off the bucket list)
Rayonier 2, Elbe, WA
Polson 70, Elbe, WA
C&C 14, Chehalis, WA
Eureka & Palisade 7, Athol, ID
Black Hills Central 110, Hill City, SD
Black Hills Central 104, Hill City, SD
Black Hills Central 7, Hill City, SD
Georgetown Loop 12, Georgetown, CO
AT&SF 3415, Abilene, KS
Sierra 3, Jamestown, CA
Rio Grande Southern 41, Buena Park, CA
Disneyland 5, Anaheim, CA
Strasburg 90, Strasburg, PA
Western Maryland 734, Cumberland, MD
B&O Museum 4, Baltimore, MD
B&O RR 25, Baltimore, MD
Lehigh Valley Coal 1, Ashland, PA
East Broad Top 15, Orbisonia, PA
W&W 98, Greenbank, DE
Southern 630, Chatanooga, TN
CN 3254, Scranton (again, is this cheating?)

Maybe not "most engines" but most mileage driven? Ha!

I am impressed! Especially interesting is Eureka & Palisade 7, which my brother and I used to play on when it was on static display in Arcadia CA in the late 1940s. And I'm glad that you had a chance to see Ventura County 2 at my "home road", Orange Empire. Santa Fe 3751 is another local sucess story--when I worked in San Bernardino in 1969-70, the "oldest Northern" sat near the Santa Fe depot, cold, silent and motionless. Here we are, 50 years after steam locomotives ceased to be a significant part of interstate commerce, able to see so many restored or maintained in operable condition.