Researching the model S modules they seem to be in 4 parallel groups at 24v a piece.
They are 6S, which means six groups of cells, with the six groups in series, and with all of the cells in each group in parallel. The nominal voltage is then six times the cell nominal voltage, or about 22 V per module.
Each group is connected in parallel by placing the cells together and all the same way up, and running a fine wire from each end of each cell, through a hole in a collector plate and welding it to the cell and the plate. The next group of cells are placed the other end up, so the positive plate for one group continues as the negative plate for the next group.
In the 12S conversions the plates are all cut into two pieces each, separating each group into two groups each with half as many cells... but then cables need to connect the plates in a new series arrangement. Even if you could find a viable place to cut each plate three times to separate the cells into 24 groups instead of 6 groups (for 24S and about 88 V per module), interconnecting the plates between the module would be a challenge.
Keep in mind in all of this work that metal shaving from cutting would be bad, and that those fine wires (which also serve as fuses) are ultrasonically welded in place. Plus, as already mentioned, that four times as many cell groups means four times as many BMS tap wires to be connected and led out of the module case.