One way to increase the statistical power and generalizability of neuroimaging studies is to collect data at multiple sites or merge multiple cohorts. However, this usually comes with site-related biases due to the heterogeneity of scanners and acquisition parameters, negatively impacting sensitivity. Brain structural connectomes are not an exception: Being derived from T1-weighted and diffusion-weighted magnetic resonance images, structural connectivity is impacted by differences in imaging protocol. Beyond minimizing acquisition parameter differences, removing bias with postprocessing is essential. In this work we create, from the exhaustive Human Connectome Project Young Adult dataset, a resampled dataset of different b-values and spatial resolutions, modeling a cohort scanned across multiple sites. After demonstrating the statistical impact of acquisition parameters on connectivity, we propose a linear regression with explicit modeling of b-value and spatial resolution, and validate its performance on separate datasets. We show that b-value and spatial resolution affect connectivity in different ways and that acquisition bias can be reduced using a linear regression informed by the acquisition parameters while retaining interindividual differences and hence boosting fingerprinting performance. We also demonstrate the generative potential of our model, and its generalization capability in an independent dataset reflective of typical acquisition practices in clinical settings.