  Tight wavelet frames (TWFs) in $L^2(\mathbb{R}^n)$ are versatile and
practical structures that provide the perfect reconstruction property.
Nevertheless, existing TWF construction methods exhibit limitations, including
a lack of specific methods for generating mother wavelets in extension-based
construction, and the necessity to address the sum of squares (SOS) problem
even when specific methods for generating mother wavelets are provided in
SOS-based construction. It is a common practice for current TWF constructions
to begin with a given refinable function. However, this approach places the
entire burden on finding suitable mother wavelets. In this paper, we introduce
TWF construction methods that spread the burden between both types of
functions: refinable functions and mother wavelets. These construction methods
offer an alternative approach to circumvent the SOS problem while providing
specific techniques for generating mother wavelets. We present examples to
illustrate our construction methods.
