It is said that Alexandros III and his successor dynasties did this a lot with their cavalry, the reasoning being that hitting first one, then before they could surround him the other two hit from his sides a little behind the lead thrust, then three and four and the like.
Even later it is said that there were rhomboid shaped formations that broke up into two wedges. Left-Right or North-South, the leads being on the central horizontal line supposedly if I remember correctly.
Is this actually feasible or if you have a wedge the most likely thing is that you are dead before even hitting your front enemy since you are focusing everyone else's attention on you by at least one second before those behind you have the chance to harm them?
The main advantage, according to the ancients, that a wedge or rhombus gave was superior manoeuvrability. Asclepiodotos says* that it's more practical than a square for the reason 'that [it] brought the leaders in front of the rest, while wheeling was thus easier than in the square formation, since all have their eyes fixed on the single squadron-commander, as is the case also in the flight of cranes'.
The ancient source also claim, however, that the narrowness of the wedge or rhombus makes it easier to break through the enemy. It's a little harder to see how this would work in practice, but this book offers a reconstruction where the leader aims for a gap in the line (especially after advancing one would have to imagine there would be a fair bit of bunching and gaps in an ancient line), which then naturally widens as the people to either side back away from the approaching horses. I don't think there's any getting past the fact that the position would be pretty dangerous, however this would have been more of a recommendation to Greek commanders than a drawback.
(source is mostly 'Soldiers and Ghosts' by J E Lendon.)
*There are a couple of detailed ancient sources on the rhombus and wedge, all are based on a lost source that is probably Posidonius (who is also a major source for early Gauls, and one of those authors I really wish had survived).