In this article, we study the scaling up of edge computing deployments. In edge computing, deployments are scaled up by adding more computational capacity atop the initial deployment, as deployment budgets allow. However, without careful consideration, adding new servers may not improve proximity to the mobile users, crucial for the Quality of Experience of users and the Quality of Service of the network operators. In this paper, we propose a novel method for scaling up an edge computing deployment by selecting the optimal number of new edge servers and their placement, and re-allocating access points optimally to the old and new edge servers. The algorithm is evaluated with two scenarios, using data on a real-world large-scale wireless network deployment. The evaluation shows that the proposed method is stable on a real city-scale deployment, resulting in optimized Quality of Service for the network operator.