As I mentioned before, I am currently taking a class on the Languages and Writing Systems of Anatolia, focusing on the ancient Hittites and some of their neighbors and successors in the region. These languages have long been recognized as part of the Indo-European language family, but they have common features among themselves which are not shared with the rest of the IE family.
Ignasi-Xavier Adiego, in Anatolian languages and Proto-Indo-European, discusses these differences in detail. One of the most striking is that the Anatolian languages do not have a separate feminine noun gender: Nouns are either neuter or “animate” (also known as “common” gender). Did Proto-Anatolian change after the separation, losing a lot of features of the ancestral language? Alternatively, perhaps Proto-Anatolian preserves the orginal forms. In this case Proto-Anatolian was the first language to separate from Proto-Indo-European. It is possible to speak of an earlier Proto-Indo-Hittite which was the common ancestor of Proto-Indo-European and Proto-Anatolian. After the separation Proto-Indo-European then innovated, and the results of those innovations are seen in the rest of the Indo-European family. This idea is nearly a century old, and I first learned about it in the 1960’s, but it seems to be attracting more attention now.
Alwin Kloekhorst, in The Anatolian stop system and the Indo-Hittite hypothesis, discusses some of the phonetic changes: Which direction did they go? Based on other examples of language change, he argues that it is more likely that Proto-Anatolian preserved the ancestral forms and Proto-Indo-European innovated rather than the other way around. This supports the Indo-Hittite hypothesis.
One source of confusion in this discussion: The ancient Phrygian language, while an Indo-European language spoken in Anatolia in the Iron Age, is linguistically not part of the Anatolian family. It is not well known, but seems to most closely related to Greek. However, the roughly contemporary Lydian, Lycian and, Carian languages, and a couple others, are part of the Anatolian family.