"Pump Handle" Half-Guard Sweep
From the same side under-hook half-guard, prop yourself on your free elbow or hand and grab their far gi such that your body is snug with theirs. Now use your prop hand to grab their far sleeve. Use your top leg to overhook their near leg, then transition to your knees, dragging their leg away from them. Pass their far arm, which you gripped earlier, between their legs to your other hand, creating a "pump handle". Use your freed hand to grab cross collar and pull turning them on their side and allowing you to obtain cross-side position.
Half-Guard to Far Single Leg
From the same position as above but your opponent has placed you in a whizzer, switch your top leg to overhook their near leg. Now use your pivot hand to hip switch, pulling your lower leg free. Drop your underhook hand to grab their far leg's toes and your pivot hand checks their knee, drive forward to place them on their back.
Inside Arm Wrap Half-Guard Sweep
If your opponent is savvy to the above, grab their sleeve with your under-hook hand, wrapping their arm around your elbow. Overhook their leg with your top leg, then pivot out freeing your bottom leg. Reach for their far knee with your free hand, most likely they will straighten this leg, i.e. "sprawling" to prevent being taken down. Now dive underneath pushing on this leg to sweep them over you to low cross-side position.
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