"Thing in itself signifies that which exists independently of our perception, that which actually is." Schopenhauer
The error here (mainly attributable to Kant) is to bestow qualities onto the 'thing in itself' that do not apply, i.e. the quality of 'thingness' and 'selfness'. Nothing exists, or does not exist, independently of our perception. 'Things' do not count without minds, nor do 'selves' — in the sense of self-contained, discreet objects — count.
The best that can be said (possibly) is that prior to or beyond the scope of perception lies a teeming cosmos of fluctuating energy that with the right biological apparatus can be rendered as discrete 'things' (perhaps Schopenhauer's 'will'). Even saying this is not sufficient, but may be as close as we can get with ideas, which in themselves are products of this process.
The practical questions are: how does the perceptual apparatus convert this teeming cosmos (which is not a 'mind-independent' thing, and neither does nor does not exist) into the things we perceive as existing, and how do we then become aware of them?