Do whatever they have a competitive edge over their rivals.
句子有误,whatever 在其引导的名词性从句被架空,它必须作成分。可以考虑改为:
Do whatever gives them a competitive edge over their rivals.
这样,whatever 引导名词性关系分句,它是一个融合性关系代词,等于 anything that,做了分句的主语,同时又做了do 的宾语。
意思:做任何能让他们比对手有竞争优势的事情。