The 2 3/4" and 3 1/2" sizes are both common. Many fixtures have screw slots for both.
A cross strap is a common way to adapt the larger size down to the smaller size. Screws to 3 1/2 box and 2 3/4 fixture mounts to strap bracket.
Some 2 3/4" boxes, particularly the metal styles, can allow a strap bracket to be mounted to the box and let the ends overhang the box so that screws on 3 1/2" centers can clear the outside of the box. In this case you can drill or open some holes under the bracket to allow the fixture mounting screws to go through the bracket and into the wall/ceiling.
You may want to also investigate the possibility to see if you can drill 2 3/4 mounting space holes in the fixture itself and forgo the use of any strap bracket itself.