Jason Morin wrote...
Here's one method. In C1 use your existing formula for
the largest number:

=LARGE(A1:A10,1)

Why not just

=MAX(A1:A10)

?

In C2 use this formula (array-entered, meaning press ctrl
+ shift + enter), then fill down:

=LARGE($A$1:$A$10,SUM(COUNTIF($A$1:$A$10,$C$1:C1) )+1)

Array formula unnecessary. Consider

=LARGE($A$1:$A$10,COUNTIF($A$1:$A$10,"="&C1)+1)