My understanding is, you have to throw enough junk ships into your fleet so that your fleet is "big enough" that additional Ordos fleets will assist. For whatever reason the Ordos have a "mercy rule" where they won't assist if there's already enough Ordos fleets for the player fleet's size or something.
Realistically though, if you're fighting triple Ordos then you should already be at +500% XP bonus, so there's not really that much reason to fight quadruple Ordos other than to just say you did it.
I don't agree with the "mercy rule", I think Ordos fleets should engage with however many fleets they have since they're supposed to be endgame (i.e. the player is supposed to know better), but that's how the game works.
(For a more technical explanation: IIRC the fleet looks at your fleet's total fleet points (this is the "fleet pts" column in ship_data.csv, which is roughly related to but is *not* the ship's deployment points, which is the "supplies/rec" column), when deciding whether or not to assist. So in theory you can take a not-used ship, such as a Kite for example, and give it say 1000 FP in ship_data.csv, which makes your fleet really big in FP, and that'll get it to assist. The problem is that FP is also used in other stuff like when the game resolves combat between two AI fleets. So if there's a Kite in one of those fleets, it'll basically automatically win over the other fleet. There may be other differences in the game when you start messing with the FP values, since they affect things like autoresolve).