Coronagraph technology is advancing and promises to enable space telescopes capable of directly detecting low surface brightness circumstellar debris disks as well as giant planets as close as in the habitable zones of their host stars. One mission capable of doing this is called EXCEDE (EXoplanetary Circumstellar Environments and Disk Explorer), which in 2011 was selected by NASA's Explorer program for technology development (Category III). EXCEDE is a 0.7m space telescope concept designed to achieve raw contrasts of 10-6 at an inner working angle of 1.2 λ/D and 10-7 at 2 λ/D and beyond. In addition to doing fundamental science on debris disks, EXCEDE will also serve as a technological and scientific precursor for an exo-Earth imaging mission. EXCEDE uses a Starlight Suppression System (SSS) based on the Phase Induced Amplitude Apodization (PIAA) coronagraph to provide high throughput and high contrast close to the diffraction limit, enabling aggressive performance. We report on our continuing progress of developing the SSS for EXCEDE, including (a) high contrast performance demonstrations at 1.2 λD, which includes a lab demonstration of 2x10-7 median contrast between 1.2 and 2.0 λ/D simultaneously with 6.5x10-8 median contrast between 2 and 4 λ/D in monochromatic light at 655nm, meeting a major milestone in our technology development program; (b) the installation of a new Low Order Wavefront Sensor (LOWFS) which enabled achieving deep contrasts at aggressive inner working angles; (c) implementation of more efficient model-based wavefront control algorithms; and (d) a preliminary broadband contrast result of 6x10-6 contrast at 1.2 λ/D in a 10% band.