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Lightweight, mesh-level models of knit fabric behavior are useful for both interactive pattern editing and initialization of yarn-level simulations. However, existing mesh-level simulation methods abstract knitting as a homogeneous material, which prevents them from capturing more complicated mixed structures. Furthermore, these methods require different simulation parameters depending on the knit pattern, or arrangement of stitches within the knit. Thus, fitting these parameters to physical examples must be done for each new pattern, even when the same types of stitches are used. To address this, we observe that physical behavior of a stitch is determined not only by its individual structure but also by the stitch types that surround it. In our work, we extend the stitch mesh model to allow for neighbor-aware material properties at the stitch level. Using structural analysis of stitch connections, we derive a finite set of four-way kernels that combine to create general knit-purl patterns for relaxation. From this, we generate a set of reference patterns that can be measured to infer the rest-lengths of the kernels using a linear model. After knitting and measuring these reference patterns, we used the derived kernel rest lengths to run relaxation on our stitch mesh models with mixtures of knits and purls that we then validated against physical examples. Our results show that the 4 neighbors of each stitch is sufficient to account for much of the neighborhood-dependent deformation, while remaining simple enough to directly fit to measured data with a set of 11 basis swatches. This allows our relaxation method to efficiently estimate the rest shape of mixed knit-purl patterns, which enables fast fabric preview and more accurate yarn-level simulation.