They all started 'on' an equal 'footing' (with one another). = They all started 'on' the same 'footing'. [=none of them had an advantage when they started]
a nation that is 'on' a friendly 'footing' with its neighbors [=a nation that has friendly relations with its neighbors]
The loose stones made it difficult for me to maintain/keep my 'footing'. [=to avoid slipping or falling]
(..) The whole world is watching us right now. Exactly. We need to alert every one of our embassies to convey to each host nation that the U.S. is on a war footing and now is not the time to test us. Patch me into -hour watch at the Pentagon. Inform the surviving joint chiefs we are going to DEFCON . (..)2016 TvShow: Designated Survivor Title: Pilot Season: 1 Episode 1