On 5 October 2016, the Missouri State Archives announced that they have a new, expanded search option for their 1910 through 1965 death certificate database. Now, for at least part of the database, you can search not only by the name of the deceased person but by the names of their parents and spouses as well. There is also a date range function available.
The Archives has started adding names of parents and spouses mentioned on death certificates with the present and is working backwards; at this time, 1965 back to 1961 is complete. They are currently indexing 1960 and will add that year as soon as it is finished. They plan to continue working back to 1910, so ultimately the entire database will be expanded.
You can see the new search engine and start using it for the expanded search at https://s1.sos.mo.gov/records/Archives/ArchivesMvc/DeathCertificates#searchDB/. If you are interested in volunteering to move things along more quickly, you can volunteer to be an indexer at https://s1.sos.mo.gov/records/archives/evolunteers/.