A plethora of single-carrier and multi-carrier (MC) CDMA systems have been proposed recently to mitigate intersymbol interference (ISI) and eliminate multiuser interference (MUI). We present a unifying all-digital Generalized Multicarrier CDMA framework which enables us to describe existing CDMA schemes and to highlight thorny problems associated with them. To improve the bit error rate (BER) performance of existing schemes, we design block FIR transmitters and decision feedback (DF) receivers based on an inner-code/outer-code principle, which guarantees MUI/ISI-elimination regardless of the frequency-selective physical channel. The flexibility of our framework allows further BER enhancements by taking into account the load in the system (number of active users), while blind channel estimation results in bandwidth savings. Simulations illustrate the superiority of our framework over competing MC CDMA alternatives especially in the presence of uplink multipath channels.