Software Product Lines (SPL) are difficult to validate due to combinatorics induced by variability across their features. This leads to combinatorial explosion of the number of derivable products. Exhaustive testing in such a large space of products is infeasible. One possible option is to test SPLs by generating test cases that cover all possible T feature interactions (T-wise). T-wise dramatically reduces the number of test products while ensuring reasonable SPL coverage. However, automatic generation of test cases satisfying T-wise using SAT solvers raises two issues. The encoding of SPLs models and T-wise criteria into a set of formulas acceptable by the solver and their satisfaction which fails when processed ``all-at-once''. We propose a scalable toolset using Alloy to automatically generate test cases satisfying T-wise from SPL models. We define strategies to split T-wise combinations into solvable subsets. We design and compute metrics to evaluate strategies on AspectOPTIMA, a concrete transactional SPL.