I have had trouble with non-standard cell types like that before. QuPath doesn’t really have a lot of options as far as cell shapes are concerned, and a deep learning or pixel classifier approach may work better (once the pixel classifier is scriptable).
Most software will detect the nucleus and then expand outward blindly by a set amount. The goblet cells just aren’t made like that. I would generally use some sort of area classifier to identify the golbet cell cluster areas, and then count nuclei within them.
One thing you could try to improve your results is the Add Intensity Features command. Rather than ROI as the area option (which searches the cell itself), use a circular tile with a set area. Run this a couple of times at different expansions (possibly using the Haralick features) to get some contextual information about the area around the cell.
A quick shot at using SLICs to classify areas, which could then be used for cell detection:
Obviously not great, though I would have needed many more images for data for the training set to make it better, given that my number of measurements was greater than the size of my training set! You may also be able to do better with the original image using accurate pixel metadata. Always easier to work in microns
*Hmm, actually playing with the pixel classifier in 0.2.0m2 I wasn’t able to do all that much better. It might be better to solve this problem using a stain for the goblet cells, though if the stain chosen is too dark, that might make it difficult to actually count the goblet cells… FastRed with a hematoxylin counterstain maybe?