Atmospheric CH₄ mole fractions resumed their increase in 2007 after a plateau during the 1999-2006 period, indicating relative changes in the sources and sinks. Estimating sources by exploiting observations within an inverse modeling framework (top-down approaches) is a powerful approach. It is, nevertheless, challenging to efficiently differentiate co-located emission categories and sinks by using CH₄ observations alone. As a result, top-down approaches are limited when it comes to fully understanding CH₄ burden changes and attributing these changes to specific source variations. δ¹³C(CH₄)_source isotopic signatures of CH₄ sources differ between emission categories (biogenic, thermogenic, and pyrogenic) and can therefore be used to address this limitation. Here, a new 3-D variational inverse modeling framework designed to assimilate δ¹³C(CH₄) observations together with CH₄ observations is presented. This system is capable of optimizing both the emissions and the associated source signatures of multiple emission categories at the pixel scale. To our knowledge, this represents the first attempt to carry out variational inversion assimilating δ¹³C(CH₄) with a 3-D chemistry transport model (CTM) and to independently optimize isotopic source signatures of multiple emission categories. We present the technical implementation of joint CH₄ and δ¹³C(CH₄) constraints in a variational system and analyze how sensitive the system is to the setup controlling the optimization using the LMDz-SACS 3-D CTM. We find that assimilating δ¹³C(CH₄) observations and allowing the system to adjust isotopic source signatures provide relatively large differences in global flux estimates for wetlands (-5.7 Tg CH₄ yr^-1), agriculture and waste (-6.4 Tg CH₄ yr^-1), fossil fuels (+8.6 Tg CH₄ yr^-1) and biofuels-biomass burning (+3.2 Tg CH₄ yr^-1) categories compared to the results inferred without assimilating δ¹³C(CH₄) observations. More importantly, when assimilating both CH₄ and δ¹³C(CH₄) observations, but assuming that the source signatures are perfectly known, these differences increase by a factor of 3-4, strengthening the importance of having as accurate signature estimates as possible. Initial conditions, uncertainties in δ¹³C(CH₄) observations, or the number of optimized categories have a much smaller impact (less than 2 Tg CH₄ yr^-1).