I came across some words for spices, hitoaji and shichimi. It occurred to me that I have never seen the terms for 2, 3, 4, 5, and 6 spices and so on. Do these terms exist?
Words of the form [number] + 味 do exist:
一味【ひとあじ】 hitoaji ≠ 一味【いちみ】 ichimi
三味 = 三味線【しゃみせん】 shamisen
五味【ごみ】 gomi "five flavours" (sweet, spicy, bitter, sour, salty)
六味【ろくみ】 rokumi "six flavours" (sweet, spicy, bitter, sour, salty, bland)
百味【ひゃくみ】 hyakumi "hundred flavours"
Shichimi is a particular blend of seven spices (chili pepper, sesame, tangerine peel, poppy seed, rapeseed, hemp seed, sanshō — of course recipes may add other / leave out some ingredients).
As @Chocolate pointed out 一味唐辛子【いちみとうがらし】 ichimi tōgarashi (or ichimi for short) is sometimes used to refer to straight chili pepper (tōgarashi) without the other ingredients.
The others (3, 5, 6, 100) don't refer to a particular blend of spices.
Kōshinryō means spice too. Though I only know this from Spice and Wolf. :P
in addition there are several synonyms of spice which use the 味 kanji, and are translated as "condiment", "flavor", "flavoring" and so on, like kōmi 香味
@Blavius (who deleted his comment) is right, the only "number" attached to 味 that means "spice" or rather "seasoning" is 七味... all other number variants would simply translate to "number of" flavors...