I am applying for H1B for the next fiscal year 2020-2021. That will be my last chance. Can I do two petitions with two different employers on same client letter?
The rule against duplicate H-1B filing is 8 CFR 214.2(h)(2)(i)(G), which says that all such petitions will be denied:
... Otherwise, filing more than one H-1B petition by an employer on behalf of the same alien in the same fiscal year will result in the denial or revocation of all such petitions. If USCIS believes that related entities (such as a parent company, subsidiary, or affiliate) may not have a legitimate business need to file more than one H-1B petition on behalf of the same alien ... USCIS may issue a request for additional evidence or notice of intent to deny, or notice of intent to revoke each petition. If any of the related entities fail to demonstrate a legitimate business need to file an H-1B petition on behalf of the same alien, all petitions filed on that alien's behalf by the related entities will be denied or revoked.
While it looks like there might be a loophole if the two petitioning companies were completely unrelated (such as not a parent company, subsidiary, or affiliate), this possibility was ruled out by the USCIS Policy Memorandum of March 23, 2018 based on the January 2018 appeal decision in Matter of S- Inc..
That decision makes clear that if two companies file H-1B petitions for the same employee to work at the same/similar position for the same end client, this is considered a duplicate filing and the rule is that both petitions will be denied. The companies will be considered 'related entities' in regard to the duplicate filing even if they are not legally related in any other way.
You can have two employers, but you would need two separate petitions.
You can find more information here: https://immigrantly.com/2014/11/25/can-i-have-two-full-time-jobs-under-concurrent-h1b/