We have just purchased a house with an old-fashioned driveway made of two ribbons of concrete with grass growing between. We would like to have a pavement that is continuous between and beyond the existing tracks. I suspect that it will be necessary to take out the old concrete, but could we avoid this work by paving between the ribbons and adding some shoulders?
The proper way is to take out the old concrete. New construction tends to settle over the years. The old concrete has most likely settled as much as it ever will. If you place new concrete adjacent to it you will get differential settlement. Besides that problem there would be no good way to match the color, texture and joints. The driveway would look like a patch job. A good subgrade is important for a properly built driveway. The Portland Cement Association publication "Cement Mason's Guide to Building Concrete Walks, Drives, Patios and Steps" gives instruction on this.