Extension of 1 month Visitor Visa

[machelon]

Hi all:
I have a little bit of a complicated situation here. My causin came 2 years ago on a tourist visa and she gave birth to a baby here. No matter what anybody thinks, I know she never intended to come here to only have the baby. After delivery she immediately left the country within the 6 month period that she had on her I-94. So she never stayed illegally even one day.
Now she came back again to help her parents, who recently became LPRs, to aclimate to their new life in the US. But at the port of entry, the Imm. officer gave her only 1 month on her I-94 and wrote NO COS (No change of Status), NO NES (No extend of status). The reasons why the officer wrote that was maybe because he did not like it that she had the baby here while being a tourist.
She would REALLY like to, and she almost has to, stay for a couple of months longer.
Can she send the petition to extend the status?, Would it have a negative effect on her future? given that she might be applying for LPR sometime in the next decade when her parents are able to sponsor her?.
If she leaves could she come back as a tourist later?

Thanks for your help.

 

[Triple Citizen]

The one month I-94 with "No COS/EOS/AOS" should be taken very seriously. The officer surely suspected her intentions. However, instead of denying her entry, he granted her a month long stay with no room for wiggling. She should promptly depart the US before her I-94 expires. By doing so, she will dispell any doubts that ICE/USCIS may have. Who knows, perhaps on her next visit she will get a full six months.
I would advise strongly against filing an I-539. It stands a high chance of being denied. That will cancel her multiple entry visa. Not worth the risk.