Modern real-time business analytic consist of heterogeneous workloads (e.g, database queries, graph processing, and machine learning). These analytic applications need programming environments that can capture all aspects of the constituent workloads (including data models they work on and movement of data across processing engines). Polystore systems suit such applications; however, these systems currently execute on CPUs and the slowdown of Moore's Law means they cannot meet the performance and efficiency requirements of modern workloads. We envision Polystore++, an architecture to accelerate existing polystore systems using hardware accelerators (e.g, FPGAs, CGRAs, and GPUs). Polystore++ systems can achieve high performance at low power by identifying and offloading components of a polystore system that are amenable to acceleration using specialized hardware. Building a Polystore++ system is challenging and introduces new research problems motivated by the use of hardware accelerators (e.g, optimizing and mapping query plans across heterogeneous computing units and exploiting hardware pipelining and parallelism to improve performance). In this paper, we discuss these challenges in detail and list possible approaches to address these problems.