Al-Hāfidh Ibn Hajr (rahimahullāh) said:
978. Narrated Ibn `Umar (radiyallahu ‘anhuma) said that Allaah’s Messenger (salallaāhu ‘alaihi wasallam) said:
“None of you should ask for a woman’s hand in marriage when his brother has already done so until the one who has already proposed leaves off his desire to marry her, or he gives him permission.”
Agreed upon, and this is the wording of al-Bukhari. (See Bukhari, no. 5142 and Muslim, no. 1412)
Shaikh Sālih al-Fawzān (hafidhahullāh) said:
This hadeeth contains within it respect and honour for the rights of the Muslims and the forbiddance of transgressing those rights. And from them is: when a man proposes to a woman. Then thereafter it is not permitted for anyone to come along and propose to her until the one who made the first proposition finishes, either because his proposal was accepted or it was not accepted, or if he gives the second proposer permission after he himself decides to step back. This is because of the fact that since he was first to propose, it became his right. So it is not allowed for anyone to transgress that and propose to her after he has proposed to her, because if one was to propose that would be considered as a transgression against the right of a Muslim. And also because this sows the seeds of animosity and hatred between the Muslims.
So it is forbidden upon a person to propose to a woman who has already been proposed to before him unless it is clear to him that the first proposer has been rejected or that the first proposer gives him permission; because that was his right first. However, if a second proposer was to come along and propose regardless of the first proposer and then was to marry her, then the majority of the Scholars hold that the marriage contract is sound and valid, even though he is sinful. Some of the Scholars such as the Dhaahiriyyah  hold that such a marriage contract is not valid.
[See Badā’i As-Sanā’i of al-Kāsāni 3/479; Bidāyatul-Mujtahid 1/754; al-‘Umm 5/62; al-Insāf of al-Mardāwayy 8/35.]
And this is just as it is forbidden for a Muslim to outbid his brother once a purchase of a commodity has concluded, or to try and buy what his brother has already bought, or to put in a counteroffer against his brother once a price has been agreed.
So these are the rights of the Muslims that it is not permitted for a person to transgress against. And for this reason, the Prophet (salallaāhu ‘alaihi wasallam) said, “when his brother has already proposed.” So brotherhood necessitates the forbiddance of transgression between brothers, and that every person respects and honours his brother.
 The Dhaahiriyyah are ascribed to Dawood b. ‘Ali al-Asbahāni Adh-Dhāhiree (rahimahullāh). They take the fiqh rulings of the Qur’an and Sunnah more “literally” than the other schools of thought. Other scholars of the Dhāhiriyyah include Abu Hayyān al-Anduloosi, Ibn Hazm al-Anduloosi (author of the famous al-Muhalla and Ihkām al-Ahkām).