Is Mileage Multiplier offered or available when flying on an AA flight but with a ticket which shows a codeshare number (eg. AA flight with JL number)?

What mileage multiplier is offered if the mileage accrual on the codeshare number is less than the mileage that AA themselves would offer if the flight were booked as an AA flight number?

As a side note, I notice (unrelated to this question) that I was offered the milage multiplier when checking in online for a domestic flight: that's new. I thought it was only offered when using a kiosk for checkin.