Which Ottoman sultan had the largest harem?

 There is only one record of the amount of concubines a Sultan had. This was Ibrahim I the mad; known for his mental condition. It is recorded he slept with 24 concubines in a single night. It is most probable also Ibrahim who had the largest harem since people abused his power.

Ibrahim with one of his concubines

For one, his empire was really strong during his lifetime, giving him lots of power and consort gifts from other nations. Secondly, people would give him concubines to distract him from the political inner affairs that were rampaging the Ottomans at the time.

It is said that this man was like a chicken in a cage. Never leaving his harem.

However, if we want to find out a more general view of other Sultans, we need to evaluate a few things:

Harem Capacity

The Topkapi Palace had the biggest harem with enough room for 400 concubines. The later Dolmabahce Palace had approximately 360 rooms for concubines. The Topkapi Palace was finished in 1465, but it hadn’t reached its full capacity only after Mimar Sinan renovated it in 1574.

Harem courtyard at the Topkapi Palace

The Dolmabahce Palace was finished in 1856, hereafter the Topkapi was used for foreign visits, viziers and other executives. Therefore we can conclude that the Sultan was reigning between 1574–1856.

Specific Elimination

This includes 18 Sultans that reign during the Topkapi, but some are left out for specific reasons:

 

Mustafa I; very short reign and crazed person

Osman II; very young, his reign was at age 13–17

Mahmud I; was recorded to have a hunchback, and was not fond of the Harem

Osman III; disliked the Harem because of his devotion for God

Abdulhamid I; also very devout to God

Murad IV; he only had one single consort

Ahmed II; he only had one single consort

Ahmed III; no haseki consorts

Now that we have 10 Sultans left, we can slowly defavor Sultans according to them having a few consorts:

Mehmed IV; only 2 consorts

Mustafa IV; only 2 consorts

The amount of consorts is not necessarily significant. Murad III had a few consorts but was renowned for being in the Harem too long.

But those two aforementioned Sultans have just a few for specific reasons; they all wrote poetry about their loveful wives. They adored them and were loyal to them.

Now that we have 8 Sultans left, we can analyze them more thoroughly. Three Sultans have a big correlation with the Harem; these are Murad III, Ibrahim and Ahmed I.

It is namely to say that Ibrahim I had the biggest harem, as per the hypothesis.
During his reign the harem expenditures increased by 28%. And the wage per concubine also got a huge raise. From 150 to 350 aspers.

Besides the people wanted him to have concubines. The people wanted a son of the Sultan so they could dispose of Ibrahim and crown a new Sultan - exactly what happened after Ibrahim got executed.