Can the husband have intercourse with one wife, then with the second wife, before washing himself?
Question

Is it permissible for a man to have intercourse with his first wife, then go to his second wife and have intercourse with her, without doing ghusl following the first intercourse?
Praise be to Allah.It is permissible for a man, if he has intercourse with one wife, to go to the second wife and have intercourse with her before doing ghusl, because of the report narrated by ‘Aa’ishah (may Allah be pleased with her) who said: I used to put perfume on the Messenger of Allah (blessings and peace of Allah be upon him) and he would go round to all his wives, then he would enter ihram in the morning, smelling of perfume. al-Bukhaari (267) 
It was narrated that Anas (may Allah be pleased with him) said: The Prophet (blessings and peace of Allah be upon him) used to go around to all his wives in one hour of the night or day, and they were eleven wives. He [the narrator] said: I said to Anas: Was he able for that? He said: We used to say that he had been given the strength of thirty men. Al-Bukhaari (268). 
And it was narrated from Anas (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) used to go around to his wives with a single ghusl. Narrated by Muslim (309). 
More than one of the scholars narrated that there was scholarly consensus on the permissibility of doing that. 
Ibn Battaal (may Allah have mercy on him) said: The scholars did not differ with regard to the permissibility of having intercourse with several wives with a single ghusl, according to what was narrated in the hadiths of ‘Aa’ishah and Anas.
End quote from Sharh Saheeh al-Bukhaari by Ibn Battaal (1/381) 
However it is preferable to do ghusl between the two acts of intercourse. 
Ahmad (22742) and Abu Dawood (219) narrated from Abu Raafi‘ that the Prophet (blessings and peace of Allah be upon him) went around to all his wives one day and he did ghusl with this one and with that one. I said to him: O Messenger of Allah, why don’t you make it one ghusl? He said: “This is cleaner and better and purer.” Classed as hasan by Shaykh al-Albaani (may Allah have mercy on him) in Mishkaat al-Masaabeeh (no. 470). 
If the man feels lazy or is not able to do ghusl, it is mustahabb for him to do wudoo’ between the two acts of intercourse, because of the report narrated by Muslim from Abu Sa‘eed al-Khudri (may Allah be pleased with him) who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “When one of you has intercourse with his wife then wants to repeat it, let him do wudoo’ between the two (acts).” 
Al-Haakim (1/254) said: Because that will give him more energy to repeat it. This additional material was classed as saheeh by Shaykh al-Albaani in Saheeh al-Jaami‘ (no. 263). 
As-San‘aani (may Allah have mercy on him) said: This indicates that it is prescribed to do wudoo’ for the one who wants to repeat intercourse with his wife. It is also proven that the Prophet (blessings and peace of Allah be upon him) was intimate with his wives and did not do wudoo’ between the two acts; and it is narrated that he did ghusl after being intimate with each one of them. All of these practices are permissible.
End quote from Subul as-Salaam (1/89) 
If a man feels lazy or is not able to do wudoo’, it is mustahabb for him to wash his private part and any areas that have been contaminated. This is emphasised if he wants to have intercourse with a wife with whom he has not yet had intercourse, because of the report narrated by al-Bukhaari (290) and Muslim (306): ‘Umar ibn al-Khattaab mentioned to the Messenger of Allah (blessings and peace of Allah be upon him) that he became junub at night, and the Messenger of Allah (blessings and peace of Allah be upon him) said to him: “Do wudoo’ and wash your private part, then sleep.” 
Imam Muslim (may Allah have mercy on him) entitled a chapter in his Saheeh: “It is permissible for one who is junub to sleep, but it is mustahabb for him to do wudoo’ and wash his private parts if he wants to eat, drink, sleep or have intercourse again” 
An-Nawawi (may Allah have mercy on him) said: 
The hadiths all indicate that it is permissible for one who is junub to sleep, eat, drink, or have intercourse again before doing ghusl. There is scholarly consensus on this point. They also indicate that it is mustahabb to do wudoo’ and wash one’s private part before doing any of these things, especially if he wants to have intercourse with a wife with whom he has not yet had intercourse, in which case it is particularly encouraged to wash his private part.
End quote from Sharh Muslim (1/499) 
Note: 
We stated above that the Prophet (blessings and peace of Allah be upon him) went around to his wives in one night with a single ghusl. 
There is nothing in this hadith to suggest that the one who has more than one wife may enter upon them and have intercourse with them all on the night that is allocated to one of them, unless he has the consent of all of them. 
An-Nawawi (may Allah have mercy on him) said: It may be said that the fuqaha’ said: The minimum division of time is one night for each wife, so how could he go around to all of them in one night? 
That may be answered in two points: 
1.That it was with the consent of all of them; there is no difference of opinion concerning the permissibility of him doing that with their consent, no matter how it is expressed.
2.Was division of time in the case of the Prophet (blessings and peace of Allah be upon him) obligatory at all times?
There is a difference of opinion concerning that among our companions. Abu Sa‘eed al-Astakhari said that it was not obligatory; rather he used to divide his time equally, and draw lots among them as an act of kindness and something that he did voluntarily, not by way of it being obligatory. But the majority said that it was obligatory. Based on the view of al-Astakhari there is no problem. And Allah knows best.
End quote from Sharh Muslim 
The third response is that which was stated by Ibn ‘Abd al-Barr (may Allah have mercy on him) when he said: 
This refers to times when he came from travelling and the like, at a time when one of them did not have a specific day, so he had intercourse with all of them at that time, then he shared his time equally between them after that. And Allah knows best, because they were free women and his Sunnah (blessings and peace of Allah be upon him) was to divide his time fairly among them, and not to be intimate with one of them on the day of another. 
End quote from al-Istidhkaar (1/263) 
And Allah knows best.