Then the cross-plane migration can handle it if it can handle zero offset. So offset is not a problem. Difficulty arises when the velocity of the earth is depth-dependent, as it usually is. Then the Jakubowicz proof fails, and so does the expedient 3-D method. With a 2-D survey you have the problem that the sideswipe planes require a different migration velocity than the vertical plane.
Rays propagating to the side take longer to reach the high-velocity media deep in the earth.
So sideswipes usually require a lower migration velocity.