Sometimes a visit must last longer: a parent falls ill, or a baby comes late. A B-2 visitor can ask USCIS (the immigration office inside the US) for more time. ESTA visitors cannot.
The I-94 decides the stay, not the visa
The visa stamp in the passport is only for coming to the US. A 10-year visa does not mean a 10-year stay.
The I-94 record shows the "Admit Until Date", the last day of the stay. Download it at i94.cbp.dhs.gov.
Count every deadline from the I-94 date.
Start early. USCIS recommends filing at least 45 days before the I-94 date. It must reach USCIS before that date. Late filing is accepted only in rare cases beyond your control.
Choose online or paper. One visitor alone can file online with a free USCIS account at uscis.gov. If both parents apply together as co-applicants, use the paper form.
Pay the fee. The current USCIS fee schedule lists $420 online and $470 on paper. Check uscis.gov/g-1055 before paying, because fees change.
Write a clear reason, such as a doctor's letter about an illness.
Add proof: a copy of the I-94, passport and visa pages, a new return ticket or booking, bank statements showing money for the extra time, and visitor insurance for the new dates.
Keep the receipt notice (Form I-797C). It proves you filed on time.
USCIS may ask for biometrics (fingerprints and a photo) at a local office. Go to the appointment.
While the case is pending
A visitor can generally stay while a timely, honest I-539 is pending.
If USCIS denies it, they must leave right away.
If they leave before a decision, the case usually ends. That is fine.
Staying after the I-94 date without a pending extension creates unlawful presence (time in the US with no permission).
The visa is automatically canceled, even after one day. A new visa usually must be requested in the home country.
Overstay of more than 180 days but less than 1 year, then leaving: banned for 3 years.
Overstay of 1 year or more, then leaving: banned for 10 years.
Save the boarding pass and e-ticket.
Check the passport stamps.
A few days after the flight, open i94.cbp.dhs.gov and choose View Travel History. The departure should appear. Airlines usually report it.
If the departure is missing, keep your proof and contact CBP to correct it before the next trip.
Counting 6 months from the visa date.
Filing the day after the I-94 date.
Throwing away the old boarding pass.