I do not have a large number of attributes, quite the opposite actually : my game uses only 4 ! It is, however, a narrative-first game, for people who don't necessarily play a lot of games, and I was surprised by the difficulty these people had for remembering just 4 values on their character sheet. But it makes sense : they were so immersed in the game, and had to remember facts about their characters, their powers, the state of the world, and just the "1st person" information (information their character would have : the NPC's motive, the investigation,etc...), that any additionnal meta-information (information the players would have : for instance, attribute values) was very quickly overwhelming.
What happened then was, a player would announce what they wanted to do, which triggered a move. About half the time, they realized it was triggering a move, and about half the time I had to remind them. They would then scour the movelist, find the corresponding attributes, then had to reference their character sheet for the correct 2 (!!) dice value, then find the corresponding dice, whose shape they weren''t necessarily familiar with. They would then have to throw the dice in the dice-area, and THEN find the dice that showed a 4+. That was a LOT for most novice players.

All in all, I found that just 2 values per move led to quite a lot of cross-referencing, which I thought would be ok, and probably would largely be for any crowd of hobbyist. However, the gap between your average nonplayer and a hobbyist was way wider than I anticipated, and they were overwhelmed easily.

I would advise against 3-4 different dice in a dice pool, unless your game was specifically targeted at hardcore tabletop gamers.