Computing several versions in a family of transformations from the same data can be seen as an instance of "diversity enhancement". One may expect from it that interesting features may pop-up better and align, while uninformative ones will appear less coherent, so that a clever (often nonlinear) combination of the different "transformed versions" would have a nicer look. In the plot below, the dotted spectra (magnitude) came from 13 different classical windows, and the black solid line is their median (rescaled by the maximum). 
Here, the result would probably have been better with one suitably-chosen window than by combining (non cleverly) randomly picked windows, because the identification of a noisy sine is a clear and well-documented problem (cf. @hotpaw2 comment on parametric spectral analysis).
However, I have found this approach to offer some robustness in cases where the signal is not too stationary, or you are not sure of the necessary window properties, or for instance in real-time sliding Fourier, when you are not sure about the memory/forgetting factor suitable for different types of transients. Using windows with different shape factors is a way to address different scales of data features (see references below in a time-frequency setting). Such approaches are at the core of several hierarchical multiscale techniques (scale-space, wavelets).
Aside analysis, multiwindow synthesis requires a careful choice of combinations. This is IMO the major flaw on the idea. They can be performed point-wise (coefficient by coefficient ) like min, max, products. Those can be seen as a form of masking. Their combination can be more complex instances of ensemble averaging, matrix factorization, etc. For instance, convolutive neural networks with different filter kernel sizes combined by pooling as an elaborate form of multiwindow processing. The last reference below is on a very recently published approach.
You can also use them at a more basic level, to have different realizations to estimate a noise level, a peak location, and this may give you a kind of heuristic confidence interval around some expected value.
A multiwindow method for generating a time-varying spectrum of
nonstationary signals is presented The time-varying spectrum is
computed from an optimally weighted average of multiple orthogonal
windowed spectrograms. The weights are determined using linear least
squares estimation with respect to a reference time-frequency
distribution. Examples are provided, with performance criteria
measures, to demonstrate and quantify the effectiveness of the method.
We extend the spectrum estimation method of Thomson (1982, 1990) to
non-stationary signals by formulating a multiple window spectrogram.
The traditional spectrogram can be represented as a member of Cohen's
class of time-frequency distributions (TFDs) where the smoothing
kernel is the Wigner distribution of the signal temporal window. We
show the unusual shape of the Cohen's class smoothing kernels
corresponding to the Thomson method multiple windows. These are a
class of smoothing kernels not hitherto used in time-frequency (t-f)
analysis. Examples of the multiple window spectrogram applied to a
noisy dual linear FM test signal and to actual underwater acoustic
data demonstrate the merit of the method.
The importance of hierarchical image organization has been witnessed
by a wide spectrum of applications in computer vision and graphics.
Different from image segmentation with the spatial whole-part
consideration, this work designs a modern framework for disassembling
an image into a family of derived signals from a scale-space
perspective. Specifically, we first offer a formal definition of image
disassembly. Then, by concerning desired properties, such as peeling
hierarchy and structure preservation, we convert the original complex
problem into a series of two-component separation sub-problems,
significantly reducing the complexity. The proposed framework is
flexible to both supervised and unsupervised settings. A compact
recurrent network, namely hierarchical image peeling net, is
customized to efficiently and effectively fulfill the task, which is
about 3.5Mb in size, and can handle 1080p images in more than 60 fps
per recurrence on a GTX 2080Ti GPU, making it attractive for practical
use. Both theoretical findings and experimental results are provided
to demonstrate the efficacy of the proposed framework, reveal its
superiority over other state-of-the-art alternatives, and show its
potential to various applicable scenarios.
