We present a systematic study of photoluminescence (PL) emission intensity and biexciton (BX) quantum yields (QYBX) in individual "giant" CdSe/CdS nanocrystals (g-NCs) as a function of g-NC core size and shell thickness. We show that g-NC core size significantly affects QYBX and can be utilized as an effective tuning parameter towards higher QYBX while keeping the total volume of the g-NC constant. Specifically, we observe that small-core (2.2 nm diameter) CdSe/CdS NCs with a volume of ∼200 nm(3) (shell comprises 4 CdS monolayers) show very low average and maximum QYBX's of ∼3 and 7%, respectively. In contrast, same-volume medium-core (3 nm diameter) NCs afford higher average values of ∼10%, while QYBX's of ∼30% are achieved for same-volume large-core (5.5 nm diameter) CdSe/CdS NCs, with some approaching ∼80%. These observations underline the influence of the g-NC core size on the evolution of PL emissive states in multi-shell NCs. Moreover, our study also reveals that the use of long anneal times in the growth of CdS shells plays a critical role in achieving high QYBX.