Etymology
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between (prep., adv.)

Old English betweonum, Mercian betwinum, "in the space which separates, midway, in the midst, among; by turns," from bi- "by" (see by) + tweonum dative plural of *tweon "two each" (compare Gothic tweih-nai "two each;" from PIE root *dwo- "two").

Between is literally applicable only to two objects; but it may be and commonly is used of more than two where they are spoken of distributively, or so that they can be thought of as divided into two parts or categories, or with reference to the action or being of each individually as compared with that of any other or all the others. When more than two objects are spoken of collectively or in divisibly, among is the proper word. [Century Dictionary]

In all senses, between has been from its earliest appearance, extended to more than two. [OED]

Between a rock and a hard place "caught in a dilemma, in a difficult situation" is from 1940s, originally cowboy slang (earlier was between the beetle (hammer) and the block, late 19c.). Between-whiles "at intervals" is from 1670s. 

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in-between (n.)
1815, "an interval;" also "a person who intervenes," noun use of prepositional phrase, from in (adv.) + between. Related: In-betweener (1912); in-betweenity (1927).
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go-between (n.)
"one who passes between parties in a negotiation or intrigue," 1590s, from verbal phrase go between in obsolete sense "act as a mediator" (1540s), from go (v.) + between.
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betweenity (n.)
"state or condition of being between," 1760, a jocular formation, perhaps coined by Horace Walpole, from between + -ity.
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tween (prep.)
also 'tween, c. 1300 as an abbreviation of between. As a noun meaning "child nearing puberty" (approximately ages 9 to 12), attested by 1988, in this case by influence of teen. Tolkien uses it in "Lord of the Rings" for "the irresponsible twenties between [Hobbit] childhood and coming of age at thirty-three." Earlier in this sense was subteen (1952). Related: Tweens. Tweenie or tweeny was a term (late 19c.-early 20c.) for "between-maid, a servant who assists two others" and was used in reference to other persons or objects in intermediary situations. And 'tween-age (adj.) was used in descriptions of clothing from 1937. Tween-ager is attested from 1946.
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*ambhi- 
also *mbhi-, Proto-Indo-European root meaning "around;" probably derived from *ant-bhi "from both sides," from root *ant- "front, forehead."

It forms all or part of: abaft; about; alley (n.1) "open passage between buildings;" ambagious; ambassador; ambi-; ambidexterity; ambidextrous; ambience; ambient; ambiguous; ambit; ambition; ambitious; amble; ambulance; ambulant; ambulate; ambulation; ambulatory; amphi-; amphibian; Amphictyonic; amphisbaena; Amphiscians; amphitheater; amphora; amputate; amputation; ancillary; andante; anfractuous; be-; begin; beleaguer; between; bivouac; but; by; circumambulate; embassy; ember-days; funambulist; ombudsman; perambulate; perambulation; preamble; somnambulate; somnambulism; umlaut.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit abhitah "on both sides," abhi "toward, to;" Avestan aibi; Greek amphi "round about;" Latin ambi- "around, round about;" Gaulish ambi-, Old Irish imb- "round about, about;" Old Church Slavonic oba; Lithuanian abu "both;" Old English ymbe, German um "around."
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*dwo- 

Proto-Indo-European root meaning "two."

It forms all or part of: anadiplosis; balance; barouche; between; betwixt; bezel; bi-; binary; bis-; biscuit; combination; combine; deuce; deuterium; Deuteronomy; di- (1) "two, double, twice;" dia-; dichotomy; digraph; dimity; diode; diphthong; diploid; diploma; diplomacy; diplomat; diplomatic; diplodocus; double; doublet; doubloon; doubt; dozen; dual; dubious; duet; duo; duodecimal; duplex; duplicate; duplicity; dyad; epididymis; hendiadys; pinochle; praseodymium; redoubtable; twain; twelfth; twelve; twenty; twi-; twice; twig; twilight; twill; twin; twine; twist; 'twixt; two; twofold; zwieback.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dvau, Avestan dva, Greek duo, Latin duo, Old Welsh dou, Lithuanian dvi, Old Church Slavonic duva, Old English twa, twegen, German zwei, Gothic twai "two;" first element in Hittite ta-ugash "two years old."

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interlingual (adj.)
"between or relating to two languages," 1854, from inter- "between" + lingual. Related: Interlingually.
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intermediate (adj.)
"being or occurring between" (two things), early 15c., from Medieval Latin intermediatus "lying between," from Latin intermedius "that which is between," from inter "between" (see inter-) + medius "in the middle" (from PIE root *medhyo- "middle").
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