  We consider two general frameworks for multiple domination, which are called
<r,s>-domination and parametric domination. They generalise and unify
{k}-domination, k-domination, total k-domination and k-tuple domination. In
this paper, known upper bounds for the classical domination are generalised for
the <r,s>-domination and parametric domination numbers. These generalisations
imply new upper bounds for the {k}-domination and total k-domination numbers.
Also, we study threshold functions, which impose additional restrictions on the
minimum vertex degree, and present new upper bounds for the aforementioned
numbers. Those bounds extend similar known results for k-tuple domination and
total k-domination.
