Survival models with changing probability distributions

Here is a Weibull PH model: $$h(t \mid \mathbf{x}) = h_0(t)\,\exp(\boldsymbol{\beta}^\top \mathbf{x}) = \gamma \lambda\, t^{\gamma - 1} \exp(\boldsymbol{\beta}^\top \mathbf{x})$$ When a time varying covariate is added, it can be written like this (for a single covariate): $$h(t \mid x_t) = h_0(t)\,\exp\!\big(\beta\, x_t\big) = \gamma \lambda\, t^{\gamma - 1} \exp\!\big(\beta\, x_t\big)$$ Is it possible to have a model where the properties of the underlying Weibull distribution changes with time? For example: $$h(t \mid x_t) = \gamma_t \lambda_t\, t^{\gamma_t - 1} \exp\!\big(\beta\, x_t\big)$$