PA,
Some light jets can still climb like a ruptured duck on one during second segment on up, or a single engine missed approach.
I still remember my right seat checkride in the Sabreliner 60, coming from older radial four engine equipment. I was very impressed with the performance. When I was given a missed approach off an ILS on one engine, I began pulling the power back on the good engine. The examiner had a fit and asked why. I had too much performance and only had three thousand feet to climb to the missed approach hold. It's a matter of perspective somewhat, there. He thought we had hardly any performance left, I thought we had too much.
A 20 series Learjet will hold 6,000 fpm in the climb easily enough, and the initial climb can exceed 12,000 fpm when light. It can hold several thousand fpm up through about FL290 or so. The cost, of course, is that you can actually see the fuel gauge move...
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that's on two engines, not one)