The track-before-detect (TBD) approach can be used to track a single target in a highly noisy radar scene. This is because it makes use of unthresholded observations and incorporates a binary target existence variable into its target state estimation process when implemented as a particle filter (PF). The PF-TBD has been extended to track two targets but only for the special case of the second target spawning from the first target. This paper proposes the extension of the recursive PF-TBD approach to detect multiple targets in low signal-to-noise ratios (SNRs). The new algorithm estimates the joint posterior probability density of all the target trajectories while keeping track of targets entering and leaving the noisy radar scene under observation using multiple modes. The algorithm's successful performance is demonstrated using a simulated three-target example.