Can a buyer's agent negotiate the cooperative fee with the listing broker?
Yes, with one exception.
Since you believe that your buyer client will love the house, you have an ethical duty to show the property even if the commission offered by the listing broker is inadequate. You can ask the listing broker to negotiate the commission; however, you may not submit an offer to purchase that is contingent upon an increase in the commission paid to you by the listing broker.
Rationale
Not only is an offer of that nature considered inconsistent with your fiduciary duty to your client, but it is also a violation of the Code of Ethics (REALTOR® Code of Ethics, Article 16-16). Your request to increase commission can be made at any time during the transaction, including after having shown the property or having submitted an offer to purchase on behalf of the client.
An Alternative Solution
You could have a conversation with your buyer client about the commission being too low to cover your expenses and costs incurred in connection with representing that client. If your client so wishes, he/she could decide to condition the property purchase offer on an agreement that the seller --not the listing broker-- pay an additional specified amount. This type of negotiation with the buyer client should only be undertaken through a written buyer representation agreement.
Often, buyer representation agreements explain that you will first seek compensation from the listing broker; however, if that amount is inadequate, you will expect the client to make up the difference. The buyer and the seller, who are the parties to the contract, can negotiate the terms as they see fit. Just make sure that your client completely understands the pros and cons of submitting an offer with that type of contingency. Also, make sure that you do not pressure your client in any manner that is inconsistent with your fiduciary duty to that client or a violation of license law.
Additional Clarification
You may ask, "Doesn't Standard of Practice 16-16 prohibit me from negotiating my commission after showing, during the purchase offer phase, or after an accepted offer?"
The answer is, "No."
Except for the fact that you cannot make an offer to purchase contingent upon a compensation increase, you can negotiate your commission with the listing broker at any time during the transaction. The REALTOR® Code of Ethics Standard of Practice 16-16 is designed to protect sellers and listing brokers by ensuring purchase offers are not held hostage by cooperating brokers demanding that the listing broker pay a higher commission. The Standard of Practice does not prohibit the listing broker and the cooperating broker from negotiating an agreement to change cooperative compensation, and that negotiation can happen before a property is shown, after showing it, or even after an offer is accepted.
The key here is that there is a dramatic difference between two brokers agreeing to change the commission --negotiating-- and making an offer contingent upon it --coercion.
You can learn more about Article 16 of the REALTOR® Code of Ethics by watching the videos linked below.
[Code of Ethics Video Series: Article 16, Part 1]
[Code of Ethics Video Series: Article 16, Part 2]
Source: National Association of REALTORS® 11/10/19.