The 1270s-80s feature various Mongol invasions of Japan (x2, unsuccessful), Vietnam (x3, unsuccessful), Burma (mixed bag), and elsewhere. They had already invaded Korea a bajillion times in the 1230s-50s (Wikipedia lists 9!) and would invade Java in 1293 (unsuccessful).

Also worth noting here is that the Mongols occupied Kashmir for decades (starting in the 1230s) and raided south into Sindh. Later, there was lots of conflict between the Chagatai and the Delhi Sultanate.

The Mongols controlled Tibet, likely through a gradual conquest beginning around 1240. There were also numerous campaigns in Siberia, Sakhalin, and other areas north of the Mongolian heartland.