Mixed model for empty cell design

Hi everybody,

I would like to do a mixed effects regression that is like this:

ISI ~ Location + Stage + Stage*Location + 1|Patient/Chan

Where Location and Stage are fixed effects, Patient and Chan are random effects and Chan is nested in Patient.

Unfortunately I don't have measures for ISI (the variable of interest) for every patient in each location.

Out of 10 Locations and 8 Patients I have:
2 locations with measures for all Patients
6 locations with 2-7 Patients
1 location with 1 Patient

Is it possible to use patient as a random effect in such a design with so many "empty cells"?

I read that mixed models can cope with empty cells but I am unable to find literature that tells me to what extent, whether the results of such a model would make sense, and if yes, how the model actually takes care of the empty cells.

Thank you in advance for your help.

Best regards,