Given that the carbon price in the EU Emissions Trading System (ETS) is only around 5€/tCO2 while consensus about a more stringent EU climate policy is very unlikely in the near future, we explore the potential scope and optimal design of additional national climate policies in the current EU policy framework. In particular, we suggest to implement a type of carbon price floor in the national EU-ETS sectors that allows for shifting emissions to non-ETS sectors like housing and transportation and retiring EU-wide emission allowances. In a simple theoretical framework with two countries and two sectors, we derive the optimality conditions for three different carbon price floor policy designs. Moreover, we are able to derive a closed form solution for the optimal price floor levels of each policy. In order to determine the empirical relevance, we conduct a numerical partial equilibrium analysis of the EU carbon market in 2020. We find that Germany shows the highest potential to reduce EU-wide cost inefficiencies and emission levels. Depending on the policy objective, Germany is able to reduce EU-wide abatement costs by 2.1% or emissions by 0.1% with a floor of 37€/tCO2 and 33€/tCO2, respectively. Finally, we find that the German climate levy proposal for old coal power plants from 2015 would have been a highly costly price floor option while its cost efficiency results are very unclear.