Here is another mode that I used to fit (two sets of sites). The parameters that the program gives off are not good even though the fitted curve nearly passes all the points.

When the standard error of the fit parameter is similar in magnitude to, or larger than, the value of the parameter, it is often because the parameter does not add any information to the fit. In other words, there are too many parameters in the model. Start with the simplest possible model (one class of sites), and only add additional parameters if (1) they improve the fit significantly (lower the chi-squared value by a statistically significant amount as per F-test), and (2) the standard error is small compared to the value of the parameter.

Also, if you already know the number of binding sites, do not fit it as an adjustable parameter. Treat it as a constant.

Do not require a perfect fit of the graph to the points. There is almost always some experimental error. Adding parameters to get a near-perfect fit could result in over-fitting.

Another reason for an unreasonable fitting result is that the starting point for the fitting is too far away from the true values, and the fitting algorithm has fallen into a meaningless "local minimum." If the program allows you to enter starting guesses for the adjustable parameters, try varying them to find the true minimum.

I agree with the answer of Adam B Shapiro

I would add another possibility: calcium ions are often bound by proteins in a cooperative manner, thus you may need to use a "sequential binding" fitting model.