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The Collaborative International Dictionary
To run on all fours

All fours \All` fours"\ [formerly, All` four".] All four legs of a quadruped; or the two legs and two arms of a person.

To be on all fours, To go on all fours, or To run on all fours (Fig.), to be on the same footing; to correspond (with) exactly; to be alike in all the circumstances to be considered. ``This example is on all fours with the other.'' ``No simile can go on all fours.''
--Macaulay.

Usage examples of "to run on all fours".

He felt the urge to hurl the axe aside and use his teeth, to run on all fours as his brothers did.