The policy is the floor, not the ceiling. If three days is what you are offered, here is how to get more.
Ask your manager before HR. Managers control things no policy mentions: deadlines, meeting loads, remote days. Make a specific request. "I need the rest of this week off, and half days next week" is easier to grant than "I need more time."
Stack your leave. Use the bereavement days first, then accrued PTO, then sick time. In Maryland, employers must let you spend earned paid leave on a death in the immediate family.[8] Colorado and Minnesota require the same for accrued sick time.[10]
Use your state's law. If you work in Illinois, Oregon, California, Washington, or Vermont, you have leave rights your handbook may not mention. See the list above. HR departments do not always volunteer them.
FMLA, if grief becomes illness. FMLA does not cover bereavement. It does cover serious health conditions, and grief that develops into depression or another condition that incapacitates you and requires ongoing treatment can qualify.[11] That means up to 12 weeks of unpaid, job-protected leave. It requires a diagnosis from a health care provider, not just exhaustion. If you cannot function, see one. You need the diagnosis for the leave, and you need the care regardless.
Negotiate the return, not just the absence. A phased return beats an abrupt one. Half days for a week. No client-facing work for two. A standing pass on one recurring meeting. Grief impairs concentration and memory for months, and a return plan that pretends otherwise sets you up to fail in public.
Put unpaid leave on the table. Many employers will hold a job through two or four unpaid weeks rather than lose a trained employee. They will rarely offer. Ask.