When I read this, my first thought was that the engine was leaning out when you push on the accelerator.

By opening the throttle, you are introducing more air into the intake, and if the fuel system doesn't match this additional air with more fuel, then the engine can lean out and act like you describe.

An 88 CE should have a CIS system. I've been running across a number of CIS systems (control head) failing recently, and the supply of good used ones seems to getting scarce. Bad used ones , however, are getting more plentiful. I can think of a couple of examples recently, where we put on thought good ones, and finally replaced that with a rebuilt unit.

Jim

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14 E250 BlueTEC black. 45k miles
95 E320 Cabriolet Emerald green 66k miles
94 E320 Cabriolet Emerald green 152k miles
85 300TD 4 spd man, euro bumpers and lights, 15" Pentas dark blue 274k miles