count date ranges that overlap

The attached worksheet gets into a similar problem I posted recently. It shows a list of stock trades. Each trade is open between < one day, to multiple days.

I need to determine how many of these trades would be open at any one time.

In the attached worksheet I've plugged in a few of what I believe to be the correct answers.

If it helps, I've deleted most of the cells that don't apply to the calcs. You'll notice that the headings of the columns I'm calculating have a "2" in them. This is my way of identifying which of 3 accounts I'm using. Once you help me out with account #2, I can do the other two.

Thanks!