I have something like that in my configuration, but it's quite language specific. For example for Golang, I have a ~/.vim/after/go.vim which contains:
syntax match goCustomParen "(" contains=cParen
syntax match goCustomFuncDef "func\s\+\w\+\s*(" contains=goDeclaration,goCustomParen
" Exclude import as function name, for multi-line imports
syntax match goCustomFunc "import\s\+(\|\(\w\+\s*\)(" contains=goCustomParen,goImport
syntax match goCustomScope "\."
syntax match goCustomAttribute "\.\w\+" contains=goCustomScope
syntax match goCustomMethod "\.\w\+\s*(" contains=goCustomScope,goCustomParen
highlight def link goCustomMethod Function
highlight def link goCustomAttribute Identifier
highlight goCustomFuncDef ctermfg=13
highlight goCustomFunc ctermfg=43
highlight goCustomAttribute ctermfg=247
highlight goCustomMethod ctermfg=33
And for Python, I have a ~/.vim/after/python.vim:
syntax match pyCustomParen "(" contains=cParen
syntax match pyCustomFunc "\w\+\s*(" contains=pyCustomParen
syntax match pyCustomScope "\."
syntax match pyCustomAttribute "\.\w\+" contains=pyCustomScope
syntax match pyCustomMethod "\.\w\+\s*(" contains=pyCustomScope,pyCustomParen
highlight def link pyCustomFunc Function
highlight def link pyCustomMethod Function
highlight def link pyCustomAttribute Identifier
highlight pyCustomFunc ctermfg=43
highlight pyCustomAttribute ctermfg=247
highlight pyCustomMethod ctermfg=33
In each case, the first block defines what is a function, a method, an attribute, and so on, the second block link these custom definition to the generic classes "Function, Identifier..." and the 3rd block defines the colors.
The files need to be in the after directory to be executed after the colorscheme and highlights definitions.
Here's a side by side comparison of with and without these settings (look on the last 3 lines):

Unless someone has a better solution, you could adapt the above for the language you need it.