This paper introduces and explores variations on a natural extension of the intensity-based doubly stochastic framework for credit default. The essential addition proposed here is to introduce a Markov chain for the “credit rating” of each firm, which is independent conditioned on a stochastic time change, or equivalently a stochastic intensity. The stochastic time change is then combined with other stochastic factors, here the interest rate and the recovery rate, into a multidimensional affine process. The resulting general framework has the computational effectiveness of the intensity-based models. This paper aims to illustrate the potential of the general framework by exploring a minimal implementation which is still capable of combining stochastic interest rates, stochastic recovery rates and the multifirm default process. Already within this minimal version we see very good reproduction of essential features of credit spread curves, default correlations and multifirm default distributions. Increased flexibility can also be achieved with a number of mathematical extensions of the basic framework. In a companion paper (Hurd and Kuznetsov, 2006) we show how the same framework extends to large-scale basket credit derivatives, particularly CDOs (collateralized debt obligations).