I was studying alpha-halogenation of ketones from LibreTexts Chemistry,
Under acidic conditions the reaction occurs through the formation of an enol which then reacts with the halogen${^1}$.
1) Protonation of the carbonyl
2) Enol formation
It also says (look at the highlighted text):
Overreaction during base promoted α halogenation
The fact that an electronegative halogen is placed on an α carbon means that the product of a base promoted α halogenation is actually more reactive than the starting material. The electron withdrawing effect of the halogen makes the α carbon even more acidic and therefor promotes further reaction. Because of this multiple halogenations can occur. This effect is exploited in the haloform reaction discussed later. If a monohalo product is required then acidic conditions are usually used${^2}$.
Why can't we just reprotonate the monohalogen in the same way as the initial ketone to form a dihalo compound?
Referance