Acceptable Offer Negotiation
If you have an offer that you are willing to accept if you are not able to change any of the terms, yet you would like to try to sweeten the offer, you should follow the path of acceptable offer negotiation.
Accept the offer ("I would like to formally request the offer..."), then put in your request to sweeten the offer ("...is there anything you can do to change _____ to _____?"). It is important to take this approach only with your new reporting manager. If the offer is made by a Recruiter or HR person, ask if you can speak with your future manager before accepting.
While this is a very soft negotiation technique and it may not work in getting the offer changed, it also preserves the offer acceptance and does not put it at risk. If you ask to change the terms of the offer without accepting, you have technically rejected the offer and made a counteroffer. The employer may decide to simply pull the offer and not proceed. So this approach is the best way to lock in your job offer while also requesting a change. If the change cannot be made, at least your manager will already be aware of your request for future consideration.
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