Exchange bias has been extensively studied in both exchange-coupled thin films and nanoparticle composite systems. However, the role of non-exchange mechanisms in the overall hysteresis loop bias is far from being understood. Here, dense soft-hard binary nanoparticle composites are used not only as a novel tool to unravel the effect of dipolar interactions on the hysteresis loop shift but also as a new strategy to enhance the bias of any magnet exhibiting an asymmetric magnetization reversal. Mixtures of equally sized, 6.8 nm, soft maghemite (γ-Fe2O3) nanoparticles (no bias—symmetric reversal) and hard cobalt doped γ-Fe2O3 nanoparticles (large exchange bias—asymmetric reversal) reveal that, for certain fractions of soft particles, the loop shift of the composite can be significantly larger than the exchange-bias field of the hard particles in the mixture. Simple calculations indicate how this emerging phenomenon can be further enhanced by optimizing the parameters of the hard particles (coercivity and loop asymmetry). In addition, the existence of a dipolar-induced loop shift (“dipolar bias”) is demonstrated both experimentally and theoretically, where, for example, a bias is induced in the initially unbiased γ-Fe2O3 nanoparticles due to the dipolar interaction with the exchange-biased hard nanoparticles. These results open a new paradigm in the large field of hysteresis bias and pave the way for novel approaches to tune loop shifts in magnetic hybrid systems beyond interface exchange coupling.