Adaptive filters are crucial in many signal processing applications. Recently, a simple configuration was presented to introduce a bias in the estimation of adaptive filters using a multiplicative factor, showing important gains in terms of mean square error with respect to standard adaptive filter operation, mainly for low signal to noise ratios. In this paper, we modify that scheme to obtain further advantages by splitting the adaptive filter coefficients into non-overlapping blocks, and employing a different multiplicative factor for the coefficients in each block. In this way, bias vs variance compromise is managed independently in each block, allowing an enhancement if the energy of the unknown system is non-uniformly distributed. In order to give some insight on the behavior of the scheme, a theoretical analysis of the optimal scaling factors is developed. In addition, several sets of experiments are included to widely study the new scheme performance.