This paper examines the effects of increasing marginal tax rates on labour supply in a setting in which workers may hold two jobs and may be constrained in their weekly hours on their main jobs. A panel data, multi-equation labour supply model is estimated with correction for tax system endogeneity and multi-sample selection in a correlated random effects framework. Data come from the British Household Panel Survey. The effects of counterfactual increases in marginal tax rates are obtained from Gauss-Seidel simulations of labour supply embedded in a tax system with allowances, tax credits, and child benefits. Labour supply to the main job is reduced by increased marginal tax rates while labour supply to the second job is increased. On net total labour supply is reduced. These effects diminish with increased marginal tax rates. In addition there are labour force withdrawal effects as well as transitions from dual job holding to unitary job holding in response to increased marginal tax rates.