Can a woman compare between more than one suitor before rejecting the first one?

It is permissible for a woman to look at more than one proposal of marriage at the same time before answering one of the suitors, because of the report narrated by Muslim (1480) from Faatimah bint Qays (may Allah be pleased with her), who said: I told him (i.e., the Messenger of Allah (blessings and peace of Allah be upon him)) that Mu‘aawiyah ibn Abi Sufyaan and Abu Jahm had both proposed marriage to me, and the Messenger of Allah (blessings and peace of Allah be upon him) said: “As for Abu Jahm, his stick never leaves his shoulder [meaning that he hits women]; as for Mu‘aawiyah, he is destitute and has no wealth. Marry Usaamah ibn Zayd.” But I did not like him. Then he said: “Marry Usaamah.” So I married him, and Allah put much good in him, and I was happy.

This indicates that she considered and thought about more than one suitor at the same time, before responding to one of them.

Once a woman has said yes to one of the two suitors, the other suitor does not have the right to approach her, if he is aware of the first proposal (and her saying yes), because the Prophet (blessings and peace of Allah be upon him) said: “No man should propose marriage when his brother has already proposed, unless the latter gives up the idea or gives him permission to propose.” Narrated by al-Bukhaari (4848) and Muslim (1412).

An-Nawawi (may Allah have mercy on him) said in Sharh Muslim (9/197): These hadiths appear to mean that it is forbidden to propose to a woman to whom someone else has already proposed. The scholars were unanimously agreed that this is forbidden if the suitor has received a clear response and acceptance, and he has not given permission [to the other man to propose] and has not given up the idea [of marrying that woman]. End quote.

This is with regard to the man; he does not have the right to propose to someone to whom another man has already proposed, unless the latter gives him permission or decides not to go ahead with the proposal.

With regard to the woman, if she thinks that someone who is more suitable will to propose to her, if she has cancelled her engagement to the first suitor, without the second one playing any role in that (by interfering or encouraging her to break off the engagement), then there is nothing wrong with her cancelling the engagement, because either party may cancel the engagement if they see fit. She should pray istikhaarah and ask Allah for guidance with regard to cancelling the engagement, and then with regard to accepting the proposal of the new suitor.

And Allah knows best.