[Note to non-semitone-box players: the following is about playing Irish music (single melody lines) on a half-step box. May or may not apply to other systems!]
You can have endless hours of fun trying to work out elegant fingering patterns that avoid the need to play two consecutive buttons with the same finger, but ultimately you will realise it cannot always be done. In fact even in places where it can be done, it's often safer and easier to just shift. The endless hours are still worth putting in, though - just make shifting a part of them.
John Redmond says at some point the same thing I tell my students, which is that if you find yourself shifting the same finger twice in a row (i.e. hitting three buttons consecutively with the same finger), it's time to take the tune apart with a few minutes of endless fun.
Use four fingers if you like, but try not doing so first
Also remember another of my pet sayings: if a passage is too hard using three fingers, try using two.
