The purpose of card systems is both speed and strength of recall.
Speed, to get through it in the time limit.
Strength, to reduce the cognitive load in forming the imagery with enough impact.
There’s a trade-off between the two.
With a high amount of images, you need more practice for speed of recall in the moment. The more images, the greater the amount of work to get them to be fast enough and distinct enough. I may be wrong - 3 even 4 digit numbers can be done that way, and I think 3 cards is only a little more complex than a 4 digit value, so maybe.
The recognition factor is another aspect: seeing one card and knowing what it’s linked with is simple, seeing two cards and knowing is slightly slower, but because it’s half the number of images to encode, it can make up the time used.
With three cards, I think the recognition time for the linked image would be significantly slower, probably making it about the same pace as a 2 card system at best. This would slow encoding rate, but it might make review in long memorisation comparatively quicker.
So with the extreme amount of distinct but easy to recall and use images needed (a major hurdle to set up, let alone memorise for speed), combined with the increased recognition speed for three cards, I think you’d need an amazing system and at best over five years of solid practice to make this work more effectively than a two card system - and even then, I think the gains would only be significant in longer card memorisation feats rather than rapidly memorising one deck, due to more rapid reviewing speeds.
It’s not impossible, but for the effort required I can’t see it being worthwhile, except once established for potentially breaking the record for number of decks memorised in a given time, which makes it very specialised.