To play more than one action at once you would need to use a sequence: http://dotween.demigiant.com/documentation.php#creatingSequence

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sequence mySequence = DOTween.Sequence();

mySequence.insert(0,currentScreenTransform.DOLocalMove(screenShowPosition,1));
mySequence.insert(0,currentScreenTransform.DORotate(screenShowRotation,1));

mySequence.Play();
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the 0 in insert is the position in the sequence you would like to place things ex:
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sequence mySequence = DOTween.Sequence();

mySequence.insert(0,currentScreenTransform.DOLocalMove(screenShowPosition,1));
mySequence.insert(0,currentScreenTransform.DORotate(screenShowRotation,1));
mySequence.insert(1,currentScreenTransform.DOPath(somepath,0.5f);

mySequence.Play();
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would do the first 2 tweens, then when they complete it would play the 3rd.


hope this helps!