You may want to define the problem a bit more. I think the most vital piece of information that would help answer this question is whether you are trying to classify patients or condition within patients (ie: "Does the patient have disease X?" vs "Is the patient in X state"?)
If you are building a model to determine whether or not a patient is in X state, then I think feature selection is not really what you should be thinking about. I would probably consider this as a batch effect problem. This makes sense in the case that you want to use as many samples as you can and therefore have multiple samples from each patient, but each patient might have different baselines or differing variation within their measurements. Therefore determining changes in the patient will be obscured unless the features are normalized within each batch.
Normally batch effects refer to difference in batches produced by different lab equipment. However, in this case, I think you could think of the patients as batches. therefore, you can check if there are batch effects by doing PCA and looking at a plot of P1 vs P2 with the samples colored by patient.If the samples are clustering together by color, then you should try correcting for batch effects by standardizing the features for each patient separately. Then redo the PCA and see if batch effects are removed.
At that point, you can just build your classification model and use feature selection or regularization as you normally would.
In the case that you are classifying the patients (ie patient has disease X or not), its clear that the difference between patients is actually what you need to build this model. I doubt that there is some rule of thumb about how many features you should use depending on the number of groups or samples within the group. You could try doing cross validation with random sampling per patient.