Split Start Date and End Date into Multiple Rows

I can have a simple table like this:

and with the following DAX I can generate a new table with rows between the two dates, on a per day basis:

DateSplitTable = 
VAR _StartDate = MIN('YourTable'[Start Date])
VAR _EndDate = MAX('YourTable'[End Date])
VAR _DateDiff = DATEDIFF(_StartDate, _EndDate, DAY)

RETURN
ADDCOLUMNS(
GENERATESERIES(0, _DateDiff, 1),
"SplitDate", _StartDate + [Value]
)

and here's the output, just as I expect:

However, what happens when I add a new column, with multiple people:

How can I take my original DAX and modify it to group by person, then split the rows? The output should look like this: