How to QC overamplified shotgun library?
FastQC (https://www.bioinformatics.babraham.ac.uk/projects/fastqc/) is a good start: it will show you observed/expected ratios for the most overrepresented sequences, and running it on a few datasets you know to be high quality should give you intuition for what looks good and what doesn't.

My labmate also produced something called preseq (http://smithlabresearch.org/software/preseq/) that uses the library complexity of an initial sequencing experiment to predict how many more unique reads you would get with additional sequencing of the same library. It could give you some intuition for whether or not it is worth sequencing your library deeper to get the information you need.