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!

Hi, I've uploaded another worksheet which attempts to describe my logic. Note that I discovered a mistake in the first worksheet,
so hopefully this new one makes better sense.

And to clarify what I mean by "open"... this means there is money invested from the moment a trade is opened, until it is closed.

Finding the max # of other, open positions during the lifespan of any particular trade helps me allocate funds invested per trade.

Please let me know if you have other questions.

Thank you!