Your diagram makes no sense. You are trying to build two power supplies: a 150V low current, and a ~20V high current. That means you will effectively have four output terminals which I think you are trying to combine. Lets call them 150+, 150-, 20+, and 20-. Are you asking if it is OK to connect 20- to 150- together to create a Common node, so that you effectively have three output terminals: +20V,+150V, and Common? The answer is yes, provided that both supplies are "transformer isolated" between their respective 120VAC line input and their rectified outputs.
Looking at your very confusing block diagram (why didn't you just post a schematic?) I do not see any transformer in the 150V supply, which means no isolation from the 120VAC to the rectified output, which means it cannot be combined with the 20V output at all. This creates a shock hazard and an instant explosion if either wire from the 150V supply touches either wire from the 20V supply.
A solution is to get a 120V-120V isolation transformer, and add that to the 150V supply.