YUP! Not a single computer! It was all shot on classic animation cameras and then put though multiple passes through optical printers for each individual effect that had to be in a scene at any given time.
Does Roger Rabbit have a shadow? Pass through the optical printer!
Does he have highlights? ANOTHER pass through the optical printer!
and so on, and so on and so on, until they got it all right, and then manually “comped” into the final film. Simply INCREDIBLE stuff!