As was shown in earlier studies, mainstream object-oriented (OO) languages C# and Java provide weaker support for generic programming (GP) as compared with functional languages such as Haskell or SML. Having explored the instruments for GP in modern OO languages Scala, Ceylon, Kotlin, Rust, and Swift, we have found out that all of them, as well as C# and Java, stick to the same approach to constraining type parameters, which we called the “Constraints-are-Types” approach. It turns out that the approach has several inevitable limitations, and because of that Haskell type classes still provide better support for GP than modern object-oriented languages do. This research is aimed to discover a mechanism that would allow to radically improve the support for generic programming in OO languages. We identify the requirements that such mechanism should satisfy, present a design of the appropriate mechanism (concept parameters), and propose a sketch of its implementation for the C# language.