Here's another example showing GEE as one way to account for the correlation between measurements from the left and right eyes in the same individuals:
Yes, possible. GEE can be used to adjust for the clustering effect (say, clustering due to enumeration areas, place, repeated measurements, etc.). You can find the details here: Article Statistical Analysis of Correlated Data Using Generalized Es...
There have been huge improvements in the the analysis of structured data in the last thirty years.
We think real world problems can be seen as combinations of three types of structure: nested hierarchy; cross classification, multiple membership. Thus pupils may be nested in schools; pupils nested within neighbourhoods, but schools and neighbourhood are crossed, and if pupils are taught by more than one teacher, the relation is a multiple membership one.
So your structure could be level 1: measurement of hand and foot , nested in individual at level 2 and crossed with the measurer (rater) also at level 2. Software can now handle such complex setups. The random effects for rater (for example) are treated as latent effects which can then be accounted for by measured characteristics ,thus by including the measured variable Prof > resident physician > student , in the fixed part of a mixed or multilevel model..
I much prefer random effects modelling of these structures to GEE, because the former approach sees the differences between units (measured by variances) and the similarity within units (measured by some intra-group correlation) as substantively interesting and not just a technical problem of getting more correct standard errors.