Laminar flame speeds at elevated pressure for methane-based fuel blends are important for refining the chemical kinetics that are relevant at engine conditions. The present paper builds on earlier measurements and modeling by the authors by extending the validity of a chemical kinetics mechanism to laminar flame speed measurements obtained in mixtures containing significant levels of helium. Such mixtures increase the stability of the experimental flames at elevated pressures and extend the range of laminar flame speeds. Two experimental techniques were utilized, namely a Bunsen burner method and an expanding spherical flame method. Pressures up to 10 atm were studied, and the mixtures ranged from pure methane to binary blends of CH4/C2H6 and CH4/C3H8. In the Bunsen flames, the data include elevated initial temperatures up to 650 K. There is generally good agreement between model and experiment, although some discrepancies still exist with respect to equivalence ratio for certain cases. A significant result of the present study is that the effect of mixture composition on flame speed is well captured by the mechanism over the extreme ranges of initial pressure and temperature covered herein. Similarly, the mechanism does an excellent job at modeling the effect of initial temperature for methane-based mixtures up to at least 650 K.