Wireless sensor networks (WSNs) are regularly used in asset monitoring applications, where the location of an asset or assets must be kept private. Providing location privacy for such an asset is tantamount to protecting the location of a source node from an attacker who is attempting to locate it. Although no solution exists to provide source location privacy over an extended period, it has been shown that attackers can be sufficiently inhibited by prominent approaches that use either a phantom node, via which protocol messages are routed, or nodes assigned to be fake sources, each of which then broadcast fake messages. However, the applicability of fake source approaches to networks where location privacy must be maintained for multiple sources has yet to be considered. This paper addresses this issue by analysing a representative fake source algorithm in the context of multiple sources, presenting simulation results that demonstrate the shortcomings of the approach and identifying the underlying limitations to pave the way for the development of algorithms capable of accounting for multiple sources.