You can get a Neulasta shot (very expensive and some insurance companies balk at paying for it) or a series of Neuropen shots (daily for a certain amount of time).
CoQ10 is supposed to help with the immune system, but ask your doctor before adding any supplement to your daily routine.
Also, I'd avoid refined sugar as it weakens an immune system. While there's not much you can do to strengthen your immunity during chemo, at least you can try to avoid weakening it any further.
My biggest struggle during chemo was with skin infections. It seemed that every little bump or scratch would get infected. I got a hangnail on a toe this last cycle and the entire toe swelled up and turned purple! Fortunately, once I was past nadir (and after days of soaking it and using triple antibiotic cream), the infection went away on its own. I've had to take antibiotics three times due to skin infections.
In light of that, I shower twice a day using antibiotic soap. I wash my bald head with antibiotic soap. I carry around hand sanitizer and use it all the time. While it would seem that none of this helped, all we can say that is if I didn't take such measures, then perhaps I would have had many more serious infections or ended up in a hospital for an infection. Thank goodness, I've not had to be hospitalized once! (One chemo cycle left!)
Avoid raw foods so that you can avoid micro bacteria that your compromised immune system might not be able to handle. Avoid large crowds and wear a mask if you are around anyone who is even slightly sick.
Best wishes to you in your journey.