Bordered Heegaard Floer homology, in its current state, can recover the hat version of Heegaard Floer homology for closed manifolds. It is related to the sutured Floer homology, and gluing sutured manifolds along surfaces with boundary. One idea for expanding the bordered framework to obtain the stronger plus/minus versions of HF, is to look at sutured manifolds and gluing along closed boundary components. I will discuss progress along this lines, as well as connections to other possible approaches.