  In this paper we describe several characterizations of basic
finite-dimensional $k$-algebras $A$ stratified for all linear orders, and
classify their graded algebras as tensor algebras satisfying some extra
property. We also discuss whether for a given preorder $\preccurlyeq$,
$\mathcal{F} (_{\preccurlyeq} \Delta)$, the category of $A$-modules with
$_{\preccurlyeq} \Delta$-filtrations, is closed under cokernels of
monomorphisms, and classify quasi-hereditary algebras satisfying this property.
