Short answer — yes. A few five‑star hotels in Mumbai explicitly run “complimentary night” offers for extended stays, while many others provide reduced rates/extra benefits for 3+ or longer stays or via loyalty/member programmes. Examples I found (with the hotel’s published offer):

• Four Seasons Hotel Mumbai — “Stay Longer – Third Night Free” (complimentary 3rd night with every two paid nights). (fourseasons.com)

• IHG / InterContinental properties — IHG launched a global “Stay 3 Pay 2” / third‑night‑free campaign for selected markets (participating IHG brands include InterContinental; check the InterContinental Marine Drive offers page for property‑level participation). (Promotion is for selected hotels/ dates; book/confirm on IHG’s site.) (loyaltylobby.com)

• Sofitel Mumbai BKC / Accor — Accor and some tour/wholesale partners have run multi‑night promotions (examples reported such as a “5th night free” partner package); Accor also offers member programmes (ALL / Accor Plus) that include free‑night/benefit options. Confirm current availability on Sofitel/Accor pages or with the booking partner. (qxtravel.io)

• Marriott family hotels in Mumbai (JW Marriott, The St. Regis, etc.) — these properties commonly publish “extended‑stay” rates and member/seasonal promotions (discounts, package deals) and Marriott/Bonvoy occasionally runs complimentary‑night promotions; check the individual hotel offer pages for any “stay X pay Y” deals. (marriott.com)

• Taj / Taj Mahal Tower Mumbai — Taj’s “Stay a Bit Longer” / similar extended‑stay packages (preferential rates and inclusions for multi‑night stays) are commonly published on their offers pages — these are usually discounts/added inclusions rather than an explicit free night, so check the specific hotel page for current terms. (tajhotels.com)

• The Oberoi, Mumbai — publishes “Extended Stay Rate” / preferential rates for 3+ nights (usually reduced rates rather than an outright free night); check the hotel’s offers page or contact reservations. (oberoihotels.com)

Notes and booking tips

• Promotions and dates change frequently (blackout dates and other restrictions commonly apply). The examples above reflect offers published on the hotels/brand pages or reputable travel outlets; always confirm availability/terms for your exact travel dates by booking on the hotel’s official site or calling the hotel. (fourseasons.com)
• Memberships often unlock the best extended‑stay deals or free‑night certificates (e.g., IHG One Rewards / InterContinental Ambassador, Marriott Bonvoy, Accor ALL / Accor Plus). If you’re a member, log in to see member‑only rates. (ihg.com)

If you’d like, I can check current “stay‑X‑pay‑Y” availability and rates for specific hotels on particular