Choosing the best functional form for variable in Cox model: an added layer of complexity

There are various approaches to choosing the function for a continuous variable in a Cox model. My problem is that I have four variables of the same type (TIL scores = measures of infiltration of different lymphocytes into a tumour). It makes sense to me to have the same function for each variable. There are two subtypes of tumour, three compartments for infiltration measure. Added to that is the univariable model and model adjusted for other covariables. Finally the best QC threshold for excluding unreliable scores is not known so I have tried 6 different thresholds. 4x2x3x2x6 is 288 models. Is it reasonably to try different functions on all 288 models and then pick the one that does best overall?

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