1st company notice period overlapped with 2nd company joining - Can any problems occur in the BGV process?

adptesting2020
Here i have one query as below so can you please advise on this.

In the journey of my career, my 1st company notice period overlapped with 2nd company joining and now I am working in the 6th company. At that time, I was facing the issue with the 1st company which not released me on time because they required me till 30th September 2011 for project requirements and in the meanwhile I joined the 2nd company on 27th August 2011 because I didn't want to lose the offer which found a better opportunity. So my release date overlaps 21 days.

The 2nd company didn't have any problem, and I informed them and both company's work shift duration was different so I was managing very well without any issue and kept confidentiality as well. And I have both companies' appointment and experience letters with proper exit formalities but here my 1st company notice period overlapping with 2nd company joining so is it ok to apply to MNC companies like TCS, Infosys, etc. Can any problems occur in the BGV process?

Please guide me on this so I can proceed accordingly.

Thank you.
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