There are a lot of promising and extensive studies about the Maitake D-Fraction, not only does it boost the immune system, it also shrinks tumors. I started taking it after my last chemo treatment, and still am, but by coincidence (cholesterol check) found out that my white blood cells and neutrophils are still AS LOW as they were during chemo - they never recovered, Maitake and all.
Before you take anything, check with your oncologist first. Mine was very adamant about me not taking anything but a multi.
I think it is very important to stay on schedule with your chemo and Neulasta seems the way to go. I was on it as well and hated the shot but was able to have each treatment on time.
Look into Maitake D-Fraction, it's the only oral 'supplement' you can take that has an impact on white blood cells (among other things). Excellent safety profile and is approved for use with all cancer treatments by the famous Memorial Sloan Kettering cancer center and also approved by the Cancer Treatment Centers of America (via the book How to Prevent and Treat Cancer with Natural Medicine).
http://www.alanpeto.com/ovarian_cancer/articles/2/1/Maitake-D-Fraction-and-Ovarian-Cancer/Page1.html