This was how it was in IITB 2-3 years ago:
In IITB, you can interview with how many ever companies you want until you get a job.
If within a particular day/slot, you have multiple shortlists, you will interview with all of them.
If multiple companies within the slot decide to extend an offer to you, your preference form that you submit the previous day will be considered. The company that wanted you but could not get you would be able to extend the offer to someone else who would have been rejected otherwise.
In most cases, the companies that offer higher packages and better profiles are given earlier days/slots. If in a rare case, a company decides to hire for a really high-paying job later, people who are already placed may be allowed to apply.
But the maximum number of jobs one can get is two and it happens very rarely because the placement team already takes care of the efficiency of days/slotting process.
I have no idea how it is in IIT Delhi, but I assume that IITD cannot be as liberal as IITB in giving people second chances as the number of companies is slightly lower. Giving people a second chance in IITD might mean that a few people will end-up not getting any jobs.
Even in IITB, only BTech and Dual Degree of CSE, Elec, Mech, and Chem get 100% placements. The other departments are sometimes left with people not finding a job.