What is the maximum amount of Valium someone can take without overdosing?

Depends. People vary as to how they respond to drugs like valium. Some will be sedated by doses that affect others very little. One variable is how much the person has been exposed to similar medication (e.g. Alcohol and benzodiazepine). Since tolerance to these medications will develop, stopping them may cause "withdrawal" symptoms, and higher doses may be needed to prevent withdrawal with ongoing use.