Yes, but this is rarely admitted.
In certain very specific situations, the case law has recognized that theextradition of a person living in Switzerland and having all his family in Switzerland may lead to a violation of Art. 8 ECHR as soon as it results in the destruction of family ties.
A recent decision of the Federal Court accepted this solution and refused extradition to Spain in the case of a mother who was taking care of her three children aged 11, 13 and 15.