Can I use a wider sill plate than what was originally used?
The sill plate is used as a transition from the wood walls to the foundation for vertical loads AND horizontal (shear) loads.
Yes, you can use a new sill plate placed on the inside of the wall (with anchors in it to hold it down to the foundation wall,) but the exterior wall sheathing needs to fasten into it too.
Horizontal shear is to resist wind and seismic events....and keep your house from floating away if it floods where you live.
Do you live in a high wind area or seismic active area?