Option 1: Select Extend tool, click on desired face of solid then click on surface. See Here for more details on the Extend tool. Note, this only works on one face at a time. If the area you want to extend is more than one face then you’ll have to use option 2.
Option 2: Select Surface Split tool, choose Two Way in Tool Options, then click on both objects in any order. Observe four surfaces resulting from the operation. Note, the image shows the four surfaces moved for clarity.
Delete the two parts you don’t need then use Stitch tool to stitch the two remaining surfaces back into a solid.
