If a traffic sign is only partially blocked, a driver may still be held responsible for seeing and responding to a partially blocked sign because drivers have a duty to be looking around.
An example of this would be a stop sign blocked by a large parked truck, but there is still a limit line, and the word STOP is painted on the ground at the intersection. Courts will ask: "what would a reasonable driver do if they see a partially blocked sign and the stuff painted on the road?" The painted word STOP on the road might be enough to make a reasonable driver stop there, despite not seeing the STOP sign itself.
In each case, it will be important to know just how much of the traffic sign was blocked, if other drivers in front of you followed or ignored the partially blocked sign, and if what you did appears reasonable and safe in those circumstances.