I did it by adding the NETWORKDAYS() function to the front of your IF()
function:
=IF(NETWORKDAYS(E$23,E$23,I2:I7)=1,IF(E$23="","",I F(WEEKDAY(E$23+1,2)5,E$23+1+(WEEKDAY(E$23+1)2)*7-WEEKDAY(E$23+1)+2,E$23+1)),"Weekend/Holiday")
.... where I2:I7 is a list of Holiday dates.