1803, "that marks distinction; making distinctions, discriminating;" see discriminate + -ory. Earlier was discriminative (1620s). As "involving distinctions based on racial prejudice," by 1954.

"multi-vehicle crash," 1929, from verbal phrase pile up "to heap up" (c. 1400), which is attested from 1849 as "to accumulate," 1899 as "to wreck in a heap" (see pile (v.)).

"riot resulting from racial hostility," by 1875, American English, from race (n.2) + riot (n.). The thing itself is older; in the Jacksonian era it was comprised in the general term mobbing.

in statistics, "involving or having two or more variables," 1928, from multi- "many" + -variate, from Latin variatio "a difference, variation, change," from past-participle stem of variare "to change" (see vary).

"racial, pertaining to a race or tribe or phylum," 1873, probably coined in German, from Greek phyletikos "of one's tribe," from phyletēs "fellow tribesman," from phylē "a tribe" (see phylo-). Related: Phyletically.

"having great multiplicity, of great diversity or variety," 1590s, from Latin multifarius "manifold," from multifariam (adv.) "on many sides; in many places or parts," perhaps originally "that which can be expressed in many ways," from multi- "many" (see multi-) + -fariam, adverbial suffix (compare bifariam "in two places"), from PIE *dwi-dhe- "making two" (from roots *dwi- "two" + *dhe- "to put, set"). Related: Multifariously; multifariousness. Earlier forms of the word in English were multiphary (adv.); multipharie (adj.), both mid-15c.

"bringing forth many young at a birth," 1640s, from Modern Latin multiparus "giving or having given birth to many," from multi- "many" + stem of parire "to bring forth" (from PIE root *pere- (1) "to produce, procure"). Related: Multiparity.

by 1852 as a term in field engineering, verbal noun from profile (v.). By 1888 as "the drawing of profiles." The racial/ethnic stereotyping sense is attested from c. 1991, American English, probably on the notion of "fitting (someone) to a profile."