Perhaps you are using the wrong ICE
ICE engines beat out steam engines because of their higher efficiencies and power densities. But the standard Otto Cycle reciprocating piston design has a significant design limitation that limits its efficiency - it does not "over-expand" during the power stroke, resulting in exhausting the hot fuel-air mixture prematurely.
The Atkinson and Miller cycle engines attempt to address this limitation by incorporating over-expansion. If you take the time to read the articles that describe these alternatives, you will see that these engines also have downsides, but have been successful in certain markets because of the efficiency.
There is a newer engine design that I have read about that seems to be a very feasible improvement over these cycles by using a rotary engine (not a Wankel) that combines over-expansion with high-power density. Not a commercial design (at least not yet) seen in the HEHC Cycle being developed by Liquid Piston. This HEHC cycle has a very limited explanation on Wikipedia, but I've read the technical backgrounders on Liquid Piston website and it sounded very appealing to me (BSME and worked at Cummins in engine design, so I have odd hobbies). Diesel engines are more efficient than equivalent gasoline engines because they can run at higher compression ratios and temperatures. The HEHC cycle can also run at high-compression ratios.
I would suggest, that in situations where you would have considered using and secondary steam turbine (clearly you are not emphasizing overall power density), you would be better off with an Atkinson engine today, and perhaps an HEHC engine in the future.
So, it's not that a secondary steam turbine would not work to improve efficiency, it's just not the most cost-effective approach.