I think there is an answer. You need to use double image to solve the problem.
Some points for you-
Mask out the cloud with shadow from your Landsat data using polygon followed by raster overlay.
Classify the Landsat image
Classify another dataset of the same area (Spot, Landsat, QB, whatever)
Join the both images. Means, fill the gap of the Landsat image (shadow+cloud) by another classified image.
Hope this helps
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