Creating calculated measure or column to identify monthly active clients

[akkitek]

Hi eveyone,
I need some help with creating a calculated measure or column in the following visual. I have a few different columns below such as Project stage, Engagement division,monthly date column(month), Project Start and End dates. I have created a date table and connected the date field to the month field. 
I have a reasonable ask but my dax calculations aren't working as required. 

The goal is to identify months in which we have active clients and how many divisions they are a part off.  A client is identified as an active client if there is a Project where Project stage = Won- Delivery and even if the Project stage is currently "Closed", the client was active in all the months between the Project start date and Project End date. So if a project is currently closed but has a start date and end date of 1/20/2023 - 12/20/23, this client was active in the year 2023. This is the part which is throwing me off.

We want to have a month or date slicer – so when we select a specific month or date range, we get all the clients which were active in that month. 

Since we have to use start and end date, I'm not sure how to connect it to my date table.  
We then want to count the number of clients with multiple engaement divisions (2 or more) as a % of the total client base (all clients with open projects)
We might want to define a field to get a count of the number of divisions for each client (incase we need to use this field later for something else) and then use that to identify clients using 2 or more divisions.
While we work on identifying/flagging the number of divisions each client is using – could we define a field that lists those divisions separated by commas? 
For example – a client that uses HR, Payroll – we could populate the field for services used using the abbreviation – like H,P
For someone using all 4 services – H,P,R,T etc.  Any help is appreciated. Thank you!
Here's a link to the test file:
https://drive.google.com/file/d/1g52TvI-kd1eK6Xaegc6O--BYj4S0zxSV/view?usp=sharing

[v-tianyich-msft]

Hi @akkitek ,

I made simple samples which you can check as follows.

An attachment for your reference. Hope it helps!

Best regards,
Community Support Team_ Scott Chang

If this post helps then please consider Accept it as the solution to help the other members find it more quickly.

[akkitek]

Hi @v-tianyich-msft ,
Thanks for helping out but I think you may have attached a different file. The above file is different from your screenshots?

[v-tianyich-msft · Accepted solution]

Hi @akkitek ,

I'm so sorry! This was my mistake, please check the attachment below.

Best regards,
Community Support Team_ Scott Chang