One thought ..
Assuming source dates (real dates) running in A1 down
Put in B1:
=IF(A1="","",IF(WEEKDAY(A1,2)=1,A1,IF(ISNA(MATCH(WEEKDAY(A1,2),{2;3;4},0)),A1+VLOOKUP(WEEKDAY(A1,2),{5,3;6,2;7,1},2,0),A1+VLOOKUP(WEEKDAY(A1,2),{2,-1;3,-2;4,-3},2,0))))
Copy down as far as required. The expression "rounds down" Tues-Thurs to Mon
& "rounds up" Fri-Sun to the next Mon.