if you don't use ajax, then use this cool feature in languges called a for loop. keep the count of partials in a hidden field, and use a submit button (not link which woudl require javascript to post) to add.

@for (Model.CurrentIndex = 0; Model.CurrentIndex < Model.MaxPartials; ++ Model.MaxPartials)
{
        @Html.Partial("thepartial")
} 

note: the parial shoud use the CurrentIndex:

   @Html.TextboxFor(m=>m.field[m.CurrentIndex])