I wouldn't assume a TA booking would necessarily be more expensive!
It MAY be.. but without checking.. how can you know?
I realise I am Down Under (and the situation may be different where you are) BUT the only bookings my TA charges a "fee" for are domestic USA flights...
My "usual" multi stop international itineraries -booked through the TA as I simply can NOT book them anywhere myself - always price at (or with very small variance from) the prices I find on ITA...
Can't hurt to simply ask!