Implement Single Linkage Clustering with Specified Initialization

Suppose I have an dataset X that I would like to implement single-linkage clustering (SLC) on. In addition to the dataset, I am given a fine-scale clustering C of the dataset.

I would like to incorporate the information contained in C into my SLC dendogram by initializing SLC with the clustering C and combining clusters iteratively based on the single-linkage linkage function. Is there a way to specify the initialization of SLC in the MATLAB built-ins?

Thank you!