Automatically store measures in a table after a refresh on a daily basis.

If you can provide examples with some sample data , it will help us to answer. Any aggregations to present persistently, I prefer doing in power query.

Since you want to do DAX, it is definitely possible. Try looking into these and see if that helps. Summarize, UNION, SELECTCOLUMNS...

DATATABLE: try checking this article

https://www.sqlbi.com/articles/create-static-tables-in-dax-using-the-datatable-function/

Random example to help you understand and say it can be done.

I am creating a table using UNION of two tables. Each table has to be same number of columns and data types. 

Table = 
UNION (
    CALCULATETABLE(
        SUMMARIZE (
            Sales,
            'Product'[Category],
            'Date'[YYYY-MM],
            "Measure", "Count",
            "Count", 'Sales Order'[Orders count]
        )
        , Year('Date'[Date]) = 2020
    )
    ,
    CALCULATETABLE(
        SUMMARIZE (
            Sales,
            'Product'[Category],
            'Date'[YYYY-MM],
            "Measure", "Sales",
            "Sales", [Total Sales]
        )
        , Year('Date'[Date]) = 2020
    )
)

Data view tab:

I hope this gives some direction. If this is not what you need, Sorry, please could you provide more info.