My current visa expires in August 2018 and I want to travel from July to September 2018 due to a family event. I have been travelling frequently to the UK and have never overstayed.
Yes. I have done so myself. I had 2 months of visa remaining. The new visa was issued without a problem.
You can apply to extend your existing visa for up to 6 months, providing you continue to meet the rules https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/673351/Visit-guidance-v7.0EXT.PDF#page36 There’s nothing in the guidance that precludes a renewal application whilst an existing visa is still valid.