The fact this is an UA MP ticket has not impact on the bag allowance.
The carrier that you first give your bags will determine the rules. Appears that would be BMI (out bound) and SAS (return). Need to see the *G allowance for each carrier.
for *G the extra allowance is
Extra Baggage Allowance - an additional 20kg (44 pounds) where the weight concept applies, or one additional piece of luggage where the piece concept applies.
Believe BMI will be the additional 20kg, not sure for SAS