How much space is left for a new family of fermions?

We perform an exploratory study of the allowed parameter range for the CKM-like mixing of hypothetical quarks of a fourth generation. As experimental constraints we use the tree-level determinations of the 3x3 Cabibbo-Kobayashi-Maskawa (CKM) elements and flavor-changing neutral current (FCNC) processes (K, D, Bd, Bs mixing and the decay b→sγ) under the assumption that the 4x4 CKM matrix is unitary. For the FCNCs we use some simplifying assumptions concerning the QCD corrections. Typically small mixing with the fourth family is favored; contrary to expectation, however, we find that also a quite large mixing with the fourth family is not yet excluded.