It is possible that you are torquing the string or the bow more when you shoot 3 under than when you shoot split. This will cause left/right misses, particularly if you're using a recurve. The tips of a recurve are more flexible than the tips of a longbow, and a slight torque will cause them to bend one way or the other, throwing the arrow to one side or the other.
A lot of times torquing is a result of simply not being aware that you're doing it. Become aware of how the bow is pressing against your hand at full draw: all the pressure of your hand against the bow should be straight forward with no sideways pressure exerted by your thumb or fingers against the handle. Become aware of how the string is pressing against your fingers at full draw: all the pressure of your fingers should be straight back, without any sideways twisting pressure against the string.
This is difficult to feel; it may feel natural to torque the string if you've gotten used to doing it. Usually a RH shooter wants to torque the string in a counter-clockwise direction, rotating the bow to a more vertical position. You can identify if this is a problem by opening up your bow hand at full draw and seeing whether the bow wants to move to a more vertical position. Ideally, you would eliminate this by relaxing your string hand so it follows the cant of the bow. If you can't relax your string hand that much, then try twisting your string hand clockwise and see what effect it has on arrow flight. It could be that when it feels like you're putting a clockwise torque on the string, you're really just taking the torque out of it. The only effective long-term solution is to relax your string hand, but there will be times when your string hand tenses up, but you can't feel the tension. If you start missing left and you can correct it by putting what feels like a clockwise torque on the string, or if the bow wants to stand up when you open your bow hand at full draw, then at least you've identified the problem and can work on relaxing your string hand.
There is nothing inherent in 3 under that should increase your left/right spread.