In his Empires of the Silk Road, Central Eurasian Studies professor Christopher I. Beckwith presents a 3-stage migratory scenario for the evolution of historical languages from the proposed Proto-Indo-European (*PIE). This is in contrast with an earlier model where the *PIE daughter languages emerged in the homeland. The homeland of the original speakers of *PIE is believed to be the Central Eurasian steppe-forest zone between the southern Urals, the Caucasus, and the Black Sea. Beckwith says that about 4000 years ago, the *PIE speakers from Central Eurasia began to migrate. There are 3 marked waves of migration, with corresponding language developments, dating from the end of the third millennium to the late second or beginning of the first. Here is my understanding of Beckwith's scenario. Please let me know of errors.
Group A. The first migration of Indo-European speakers spread southwards to the Caucasus and Black Sea where there were already non-Indo-Europeans. Some continued further to become the ancestors of the Tokharians and Anatolians. They mixed with the native populations developing creole dialects. The most important of these was Proto-Indo-Iranian and the central area where it developed was the Bactria-Margiana Culture.
Group B. Indo-Iranians were influenced by a non-Indo-European language that led to Proto-Indic. Conflict between Proto-Indic and Proto-Iranian speakers developed. Iranians defeated the Indians and drove them to the edges of Central Eurasia. Speakers of Indic and others from the homeland migrated, intermingled, and produced new creoles. This was when the speakers of Mitanni and the Mycenaean Greeks enter recorded history. The end of this period saw the Iranians in control of the Central Eurasian steppe and the Germanic peoples in Central Europe.
Group C. The third migration consisted of Celtic, Baltic, Slavic, Albanian, and Iranian people from the Central Eurasian homeland. [It is unclear how they came to be differentiated prior to leaving the homeland, but presumably it is after-the-fact naming.] The Celtic, Albanian, Slavic, and Baltic people moved west, northwest, and north; while the Iranians went after the Indians who were in the Near East. They may also have crossed Central Asia into China.