I've down a lot of international trekking. Peru comes to mind first. You can get away from the crowds by sticking to the shoulder seasons in the Cordilleras Blanca, Huayhuash and Vilcanota. (May, Sept-Oct) You can arrange for locals to resupply you on certain dates with their pack animals, and you can certainly explore for a couple hundred miles (few weeks). I would place the cordillera Vilcanota at the top of the list. You can do a very extensive trip around Auzangate and going out as far as Quelcayya ice cap. Many high passes are becoming ice free due to global warming which is permitting circuits that where much more difficult before.
Nepal as well ( Rowaling, Kanchenjunga); India ( think Ladahk, Zanskar, in September / October cold but quiet)Sikkim; China:Yunnan nice hike around Kawagebo with thousands of Tibetan pilgrims); Kyrgyzstan: hike along the western side of the Tien Shan easier to access than western China.