A root for “brother” that Tolkien introduced in notes on finger-names from the late 1960s as a companion to √NETH “sister” (VT47/14, 26, 34). It conflicts with, and possibly replaces, earlier uses for √KHAN such as √KHAN “back” in notes from around 1959 serving as the basis for the prefix Q. han- in hanquenta “answer” (PE17/166). The root ᴹ√KHAN also appeared in The Etymologies of the 1930s glossed “understand, comprehend”, with various derivatives in both Quenya and Noldorin of similar meaning (Ety/KHAN).
It is unlikely that all these uses of √KHAN coexisted, but I think at a minimum both √KHAN “brother” and ᴹ√KHAN “understand, comprehend” should be retained for the purposes of Neo-Eldarin, as the latter has no good replacements in Tolkien’s later writing. As for hanquenta “answer”, it might be reinterpreted as “a saying providing understanding”, and so be derived from ᴹ√KHAN “understand”.
This root appeared in various notes from the late 1960s as the basis for the particle of uncertainty Q. cé. This particle meant “if” or “maybe” in various contexts, but in notes from 1969 √KE was given the sense “may (be)” and paired with √KWI “suppose”, which was the basis for qui “if” (PE22/158). This can be compared to another paradigm also from 1969 associated with the Ambidexters Sentence where cé meant “if” and it seems the root √keye (with derived verb cíta-) meant “suppose” (VT49/19). Of the two paradigms, I think √KE “maybe”/√KWI “if, suppose” is more useful for the purposes of Neo-Eldarin, but it seems Tolkien’s own thoughts on the subject were in flux.
In notes written in 1967, Tolkien gave what was apparently an inverted form of this root, √ek “it is open”, from which the impersonal Quenya verb ec- “may, can” in the sense “have the opportunity to” is derived (VT49/20). This inverted form is almost certainly related to √KE, as suggested by Patrick Wynne.