A new form of the filter bank multi-carrier spread spectrum (FBMC-SS) waveform is presented. This new waveform modifies the filtered multi-tone spread spectrum (FMT-SS) system, and is intended to whiten the power spectral density (PSD) of the transmit signal. In the conventional FMT-SS, subcarrier bands are non-overlapping, leaving a spectral null between the adjacent subcarrier bands. To make FMT-SS more appealing for a broader set of applications than those studied in the past, we propose adding additional subcarriers centered at these nulls and thoroughly explore the impact of the added subcarriers on the system performance. This modified form of FMT-SS is referred to as overlapped FMT-SS (OFMT-SS). We explore the conditions required for maximally flattening the PSD of the synthesized OFMT-SS signal and for cancelling the interference caused by overlapping subbands. We also explore the choices of spreading gains that result in a low peak-to-average power ratio (PAPR) for a number of different scenarios. Further reduction of the PAPR of the synthesized signal through clipping methods is also explored. Additionally, we propose methods of multi-coding for increasing the data rate of the OFMT-SS waveform, while minimally impacting its PAPR.