This article focuses on the number of support points in the optimal design class for multi-exponential regression models. A special design setup is proposed which allows different starting points for each subject. It serves as a useful tool when subjects have different timelines and offers more flexibilities compared to the usual clinical designs. Autocorrelated covariance structure is accommodated to address the correlations among different observations for a single subject. The upper bounds of the cardinality of design support have been determined for one-compartment PK model and bi-exponential model.