The initial guess for the binding affinity was likely inaccurate, which is why the data didn’t fit well at first? I assume the goal of the analysis is to refine the model parameters to accurately determine the binding affinity that best represents the observed interaction. Adjusting parameters during data fitting is not manipulation but a necessary part of the process when the dissociation constant is unknown. After all, if the true binding affinity were already known, what would be the purpose of conducting the experiment? However, this approach would assume that other parameters, such as concentrations and injection volumes, are well-controlled and not varied during the fitting process. Varying multiple parameters simultaneously during fitting can be problematic, as it increases the risk of overfitting and may result in a model that fits the data but does not accurately reflect the underlying chemistry. If you have literature data indicating the expected range of the dissociation constant, and your system deviates significantly, you should consider whether other experimental parameters might be influencing the results. For example, in protein-metal binding experiments, if the buffer can complex with the metal, it could significantly affect the observed metal-protein binding. Similarly, physicochemical factors such as ionic strength, pH, and temperature at which ITC experiments are preformed can also play critical roles in binding interactions. Without seeing the binding curves, it is hard to definitively tell, but if there is no clear evidence for a specific binding stoichiometry (and there are no strong indications in the literature that the one stoichiometry is always achieved for such systems), it may be reasonable to explore a multiple-site binding models.

Without an image of the thermogram and the binding isotherm is difficult to make a suggestion about your question. I can imagine, but a picture will help.