Should I modify the existing index to include all three columns or create a completely new one?
It depends on the way you query the table.
Assume you have below index..
create index nci on tablea(Col1,col2)
below queries will satsify the index
select * from table1 where col1=1 and col2>10
select * from table1 where col1=1 and col2=10
below query wont satisfy above index
select col1,col2 from table1 where col1>40 and col2=40
So second column is not useful ,if you use any comparison other than equality on first column.The same applies if you add third column
In summary, you can add third column ,if you need your queries to be covering and also they fall into above sample category(equality on first column)..