Yes, it is possible. The most carried out transplantation of living donors, is the transfer of a kidney and a part donation of a liver. This is possible between family- members and loved ones. It's elemental, that the donor is healthy, bloodgroup compatible and that the tissue criterias are matching with the recipient.
It's also possible to make an altruistic donation. Therefore an anonymous person is donating an organ, like kidney or part of liver, for free and out of altruism.
Living small bowel- and living lung lobe-transplantation are not very frequent in Switzerland.