We construct a family $\fancyscript{F}$ , indexed by five integer parameters, of finite monogenerated left-distributive (LD) groupoids with the property that every finite monogenerated LD groupoid is a quotient of a member of $\fancyscript{F}$ . The combinatorial abundance of finite monogenerated LD groupoids is encoded in the congruence lattices of the groupoids $\fancyscript{F}$ , which we show to be extremely large.