Widely utilized in the field of Neuroscience, implantable neural recording devices could capture neuron activities with an acquisition rate on the order of megabytes per second. In order to efficiently transmit neural signals through wireless channels, these devices require compression methods that reduce power consumption. Although recent Compressed Sensing (CS) approaches have successfully demonstrated their power, their full potential is yet to be explored. Built upon our previous on-chip CS implementation, we propose an energy efficient multi-mode CS framework that focuses on improving the off-chip components, including (i) a two-stage sensing strategy, (ii) a sparsifying dictionary directly using data, (iii) enhanced compression performance from Full Signal CS mode and Spike Restoration mode to Spike CS + Restoration mode and; (iv) extension of our framework to the Tetrode CS recovery using joint sparsity. This new framework achieves energy efficiency, implementation simplicity and system flexibility simultaneously. Extensive experiments are performed on simulation and real datasets. For our Spike CS + Restoration mode, we achieve a compression ratio of 6% with a reconstruction SNDR > 10 dB and a classification accuracy > 95% for synthetic datasets. For real datasets, we get a 10% compression ratio with ∼ 10 dB for Spike CS + Restoration mode.