Jang-A-Lang. You can't DD on CPST because it is a wildcard. And DD on wildcards are not allowed. But to answer your question from a general perspective.
If you decide to Double down on a stock you will get the closing price of today if you entered in the trade before 4pm today. So obviously it would lower your cost basis if your original shares where acquired at higher prices. However to me they are two separate units, that is the way I appraoch it. Example Below.
Example of stock a- I assumed the new shares were brought by a position that was breakeven, when sold to keep it simple.
orig 500 shares @ $2.00
New 625 shares @ $1.60
Position 1125 shares @ $1.7778
So as you can see your cost basis would drop. However in my setup they are two different positions so I don't calculate the cost basis of the position, because I don't have to, as it is easier to leave them too separate positions. Hope this helps.