The fourth partner is Mary Beer, the former marketing director of Flextech and creator of the marketing strategy for Bravo and Living TV.
The Drugstore starts with projects for Selfridges, Coca-Cola, Abbey and the men's fashion label Hope & Glory.
The Drugstore has been born out of the former Cave Anholt Jonason agency, which closed in June 2001.
Cave bought the equity held by his erstwhile associates, Simon Anholt and Joakim Jonason, and has since been building up a stable of creative talent to work on communications projects.
The new agency will operate by analysing a communication brief and working out the best way to execute it across a range of disciplines.
Cave said: "Clients and agencies acknowledge that the current agency structure is too inflexible but nobody does anything about it."