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The fast and dynamic evolution of e-retailing is driving structural changes in the way companies are reaching the urban consumer. Companies are offering faster delivery services, deploying collection-and-delivery points and multi-echelon distribution networks with a range of facility types, diversifying last-mile transportation modes with new types of vehicles and contracting third-party and crowd-sourcing-based transportation. In this paper, we propose an integrated modeling framework for strategic last-mile design of three-tiered multi-modal networks in omni-channel environment, with customer demand differentiated according to multiple time-differentiated delivery services and multiple product-exchange alternatives. In order to apply this framework in a large-scale demand setting and capture the granularity of customer demand and distribution network features, we extend the route cost estimation formulae from the literature and incorporate them in a three-echelon capacitated location-routing problem that optimizes the configuration of distribution networks in an integrated way. Through a number of numerical experiments, we show the impact of the diversified customer demand and the novel distribution network features on the overall network performance and demonstrate the economic benefit of an integrated approach. A real-world case study, inspired by the ongoing operations of a major omni-channel retailer in São Paulo, Brazil, serves to illustrate the real-world impact of our work.