We've already got the LDS Pioneers, for those who crossed the Plains to Utah by wagon or on foot before the transcontinental railroad was finished in 1869. There's also a subcategory related to the LDS project for the Mexican Colonias, settled by Mormons who headed for Mexico when the US started jailing polygamists in the 1880s. I've spent a few months working on the Mormons, and have ended up wondering what motivated them to leave Europe (Scandinavia & England especially) in a fair-sized stream. And Scandinavian immigrants generally - nowadays there's a Scandinavian-themed gathering in Minot, ND that draws 60,000 people annually, mostly from the northern plains. (Their nametag motto is "Hi, and where are you from?" Yes, they have nametags.)
One of my long-standing interests is the patterns of migration & settlement in the US. There's the Dust Bowl refugees, although a lot of the Okies and Arkies were actually displaced tenant farmers who got tractored out. Some went west to California, which continued through the WWII years and beyond. Others headed north, black & white, and worked in steel and auto & so on mostly up the Mississippi to the Ohio River Valley & Great Lakes. They hopped freight trains as the railroad expanded.
I read an informative book awhile back "The Worst Hard Time" by Tim Egan about the people who did not leave the Dust Bowl area (W Kansas, OK & TX panhandles, NE New Mexico, Colorado plains.) He talked about the "Volga Germans" who came to Russia under Catherine the Great (also German) who gave them special incentives and exemption from various obligations. After she died, those privileges had no one to defend them, and there ended up being a migration to the US high plains, much of what became the Dust Bowl as it happens. (They brought winter red wheat to the US, and also tumbleweeds aka Russian thistle amongst their seed wheat.)
We've had some "forced"migrations in and to the US, too. One would probably have better luck tracing Cherokees and the rest of the Five Civilized tribes through the Trail of Tears than with the trans-Atlantic slave trade of Africans to the Americas.
The prisoners sent to Australia from Britain are a big population transfer, though not technically a "migration." More recently, the Nazis engendered a variety of refugees in abundant numbers, mostly Jews and Eastern Europeans of various nationalities. There's a steady stream of refugees from the Middle East in recent decades, most recently from Syria. "Shanghai" became a verb in addition to the name of a Chinese city, describing how people got pressed into service to build the US trans-continental railroad. It would be interesting to look into how Japanese-American lives were radically changed by US internment camps.
There's also English colonial-era migrations to the US in addition to PGM, as explored in depth by David Hackett Fischer in "Albion's Seed": Scots-Irish, royalists fleeing the Cromwell period, Quakers to PA/NJ. I have a line of ancestors who went to Canada after the American Revolution - and I've read that there was a migration of royalists at that time. The Acadians came from French Canada to Louisiana and became Cajuns. There's various Spanish/Mexican-related movements, too, going back before any of the English settlers. There's the Irish migration because of the potato famine.
IMO, most of the early settler migrations within the US have been motivated mostly by people wanting their own land. New England got full, and so they headed for the Great Lakes region, and then beyond. It's an aspiration which has largely faded from memory as so many people have now left the farm and headed for the cities.
Looking forward, there's predictions of 100s of millions of "climate refugees" over the next several decades. There's already some islands which have had to be abandoned, Alaskan villages have problems from a shortened ice season as well as rising sea levels. It is predicted that there's island nations which will simply cease to exist due to rising waters.
Not all of these are easy to document, and there's plenty more. No shortage of ideas!