Dax formula combining different filters

Hello romovaro. 
If I'm understading the scenario correctly, I think you can create a table with the following DAX:

Booked by Project Team = 
VAR MeetsFirstRequirement =
    CALCULATETABLE(
        VALUES( 'BMPS LOF Report'[CUID] ),
        CONTAINSSTRING(
            'BMPS LOF Report'[TASK],
            "Start Partner Engagement"
        )
            && 'BMPS LOF Report'[TASKACTUALPERFORMER] = "Robert Monte"
            || 'BMPS LOF Report'[TASKACTUALPERFORMER] = "Maria Wells"
    )
VAR MeetsBothRequirements =
    CALCULATETABLE(
        VALUES( 'BMPS LOF Report'[CUID] ),
        MeetsFirstRequirement,
        'BMPS LOF Report'[TASK_STATUS] = "Closed",
        CONTAINSSTRING(
            'BMPS LOF Report'[TASK],
            "Partner Acknowledgement"
        )
    )
RETURN MeetsBothRequirements

One issue that I had was that if I am understanding correctly, then none of the CUIDs in your sample table met the requirements, so the result was coming up blank. For testing, I changed the status from "Received" to "Closed" on Row 5 (which is the Partner Acknowledgement row for CUID 1000543IT01), so that it would meet both requirements,.

The results look like this:

I saved a .pbix here that you can download if it is helpful.

Here is the original data, with the value I changed highlighted:

Hi romovaro. Thanks for the additional info. I think I'm understanding now.

Give this a try:

Booked by Project Team =
VAR MeetsFirstRequirement =
    CALCULATETABLE (
        VALUES ( 'BMPS LOF Report'[CUID] ),
        CONTAINSSTRING (
            'BMPS LOF Report'[TASK],
            "Start Partner Engagement"
        )
            && 'BMPS LOF Report'[TASKACTUALPERFORMER] = "Robert Monte"
            || 'BMPS LOF Report'[TASKACTUALPERFORMER] = "Maria Wells"
    )
VAR MeetsBothRequirements =
    CALCULATETABLE (
        VALUES ( 'BMPS LOF Report'[CUID] ),
        MeetsFirstRequirement,
        'BMPS LOF Report'[TASK_STATUS] = "Closed",
        CONTAINSSTRING (
            'BMPS LOF Report'[TASK],
            "Partner Acknowledgement"
        )
    )
VAR Result =
    ADDCOLUMNS (
        MeetsBothRequirements,
        "Date Closed",
            CALCULATE (
                MAX ( 'BMPS LOF Report'[TASK_COMPLETED_DATE2] ),
                'BMPS LOF Report'[TASK_STATUS] = "Closed",
                CONTAINSSTRING (
                    'BMPS LOF Report'[TASK],
                    "Partner Acknowledgement"
                )
            )
    )
RETURN
    Result