1. advance something to a higher or more serious level
bring/take the matter further
When you 'take something further', you escalate an issue or bring a complaint, grievance or action to a higher level. Usually, this phrase is used to talk about bringing problems to a higher power to resolve them; or to encourage someone to deal with them. It can also be used to talk about doing something at the highest level, such as a sport or an action. You can take your education further, for example, or bring your 'game' further.