Where did we get the "fours" in "on all fours"?

In the OED Third Edition, September 2012, the (updated) etymology given under the headword all fours, n. suggests three routes for the -s attachment.

1. With reference to the four legs of an animal, the alteration of 'all four [legs]', adj. + adj., to 'all fours' might be explained by the omitted but understood plural noun, 'legs'. The earliest use evidenced for 'all fours' in this sense is 1678.

This is probable.

2. The -s suffix forming adverbs may also have played a role:

... Hence there arose in early Middle English mixed forms such as aȝeines, amiddes; and the frequent coexistence of the two forms of the same adv., one with and the other without s, led to the addition of s to many advs. as a sign of their function. In some instances the extended form prevailed, as in eftsoons; in others it survived only in dialects, as in oftens, gaylies (Scottish).

This is perhaps probable.

3. The earliest use of 'all-fours', in 1674, refers to the name of a card game:

... in which four game points are available per round: for being dealt the highest trump, being dealt the lowest trump, taking the Jack of trumps, and winning the most tricks.

About this sense, the OED suggests that its use "may have influenced the use of the" -s forms in both the sense 'on or upon all fours' with reference to the four legs of animals and the sense 'to run on or upon all fours'. The OED also suggests that this sense "may show an independent formation" from the adj. 'all' and the plural of the noun 'four'.

This is possible.

After looking at the evidence and reading the analysis presented in the OED, I favor the explanation that all of the suggested influences played a role in the adoption and retention of the -s form. Of those influences, I am biased toward the last, the use and historical prevalence of the name of the card game 'All-Fours', as the most dominant. My bias arises mostly from that being the earliest evidenced use of the -s form.

The World Wide Word suggests that the "s" was introduced in the 19th century suggesting the four legs or extremities:

• The image behind it is that of a dog or similar animal. If it has use of all four legs, it runs smoothly and evenly, as opposed to the way it would limp if one of its legs were damaged. The expression was originally on all four, known from the sixteenth century in phrases we’re still familiar with, such as to crawl upon all four (the final “-s” was added in the nineteenth century; earlier, a word such as “legs” or “extremities” was understood).

• In the eighteenth century, people started to use to run on all four as a figurative expression to describe some proposition or circumstance that was fair or equitable, well-founded, sturdily able to stand by itself. To be on all four or to stand on all four meant to be on a level with another, to present an exact analogy or comparison with something else (presumably the image is of two animals standing together, both on all four legs, hence in closely similar situations).

• It’s hardly common now outside the legal profession, and I suspect from what subscribers have told me that it doesn’t turn up that often these days even in that field.

This is confirmed by The OED which notes the 19th-century s-addition,

• [formerly all four, sc. extremities. The -s was added prob. during the 19th century; not in Johnson 1808.]

• invokes a metaphor of the form "not limping = fair or even, not lame", and gives an earlier citation, from a British legal context, which also involves running, and is applied to a comparison:

  • fig. to run on all fours, i. e. fairly, evenly, not to limp like a lame dog. to be, or stand, on all fours: to be even or on a level, to present an exact analogy or comparison (with).

  • 1877 Daily Tel. 15 Mar., It must stand on all fours with that stipulation._

  • [1883 Daily News 8 Feb. 3/7 The decision I have quoted is on all fours with this case.

(itre.cis.upenn.edu)

We say "modal verbs" and often speak in shortened form of modals. Though "modal" is an adjective we add the plural-s of "verbs" to "modal" and create a new noun in plural.

I think that the same process took place when "moving on all four limbs/extremities" was shortened to "moving on all fours".