  Framelets (a.k.a. wavelet frames) are of interest in both theory and
applications. Quite often, tight or dual framelets with high vanishing moments
are constructed through the popular oblique extension principle (OEP). Though
OEP can increase vanishing moments for improved sparsity, it has a serious
shortcoming for scalar framelets: the associated discrete framelet transform is
often not compact and deconvolution is unavoidable. Here we say that a framelet
transform is compact if it can be implemented by convolution using only
finitely supported filters. On the other hand, in sharp contrast to the
extensively studied scalar framelets, multiframelets (a.k.a. vector framelets)
derived through OEP from refinable vector functions are much less studied and
are far from well understood. Also, most constructed multiframelets often lack
balancing property which reduces sparsity. In this paper, we are particularly
interested in quasi-tight multiframelets, which are special dual multiframelets
but behave almost identically as tight multiframelets. From any compactly
supported \emph{refinable vector function having at least two entries}, we
prove that we can always construct through OEP a compactly supported
quasi-tight multiframelet such that (1) its associated discrete framelet
transform is compact and has the highest possible balancing order; (2) all
compactly supported framelet generators have the highest possible order of
vanishing moments, matching the approximation/accuracy order of its underlying
refinable vector function. This result demonstrates great advantages of OEP for
multiframelets (retaining all the desired properties) over scalar framelets.
