At Constant IAS, TAS rises. Your consumption per NM decreases since you are travelling more miles per unit of fuel consumed at the higher altitude.
This however has its limits in regards to available power of the engine as it relates to maintaining IAS, also Recip engines begine to lose efficiency due to other non monitored aspects of the engine (higher induction air temperatures, exhaust backpressure etc).
Since you mention constant (I assume Stoichiometric) fuel ratio which I assume this relates to an otto-cycle engine this can decrease your overall efficiency due to more wasted fuel consumed as a result of maintaining combustion stability. Otto-cycle engines are very inefficient since fuel air ratios are relatively fixed over a very narrow range of power output. Lower power lean of peak operation opens up the range but still has little effect on overall fuel consumption or aircraft range due to decreased IAS/TAS.
Variable fuel ratio engines Diesel, Turbine, GDI/FSI have wider fuel ratio ranges closely related with load thus they always run significantly leaner in the higher load regimes netting greatly imrpoved thermal efficiency double that of an otto-cycle engine ie gasoline recip.
DB