A significant amount of research studies in the past years has been devoted on developing efficient mechanisms to control the level of degradation among consolidate workloads in a shared platform. Workload consolidation is a promising feature that is employed by most service providers to reduce the total operating costs in traditional computing systems [1]-[3]. Serverless paradigm - also known as Function as a Service, FaaS, and Lambda - recently emerged as a new virtualization run-time model that disentangles the traditional state of applications' users from the burden of provisioning physical computing resources, leaving the difficulty of providing the adequate resource capacity on the service provider's side. This paper focuses on a number of challenges associated with workload consolidation when a serverless platform is expected to execute several data-intensive functional units. Each functional unit is considered to be the atomic component that reacts to a stream of input data. A serverless application in the proposed model is composed of a series of functional units. Through a systematic approach, we highlight the main challenges for devising an efficient workload consolidation process in a data-intensive serverless platform. To this end, we first study the performance interference among multiple workloads to obtain the capacity of last level cache (LLC). We show how such contention among workloads can lead to a significant throughput degradation on a single physical server. We expand our investigation into a general case with the aim to prevent the total throughput never falling below a predefined utilization level. Based on the empirical results, we develop a consolidation model and then design a computationally efficient controller to optimize the throughput degradation among a platform consists fs multiple machines. The performance evaluation is conducted using modern workloads inspired by data management services, and data analytic benchmark tools in our in-house four node platform showing the efficiency of the proposed solution to mitigate the QoS violation rate for high priority applications by 90% while can enhance the normalized throughput usage of disk devices by 39%.