How much space is left for a new family?

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 3 $\times$ 3 CKM elements and FCNC processes ($K$-, $D$-, $B_d$-, $B_s$-mixing and the decay $b \to s \gamma$) under the assumption that the 4 $\times$ 4 CKM matrix is unitary. For the FCNCs we use some simplifying assumptions concerning the QCD corrections. Typically small mixing with the fourth family is favoured, but contrary to expectation we find that also a quite large mixing with the 4th family is not yet excluded.