You seem to be in good shape. Just check a few of the adjacent states, as suggested by JTSD20. You may just get lucky. If not, try not to worry, everything else looks good.

Just a few things to note:

If your great grandparents arrived in the US as children, you will need to trace back to THEIR parents to ensure that either or both did not receive derivative naturalization through the naturalization of their parents. Do the censuses list them as “A” (Alien)? (When ...

Were your grandparents and great grandparents married in Italy or in the US? Do you know where they were married? Is it possible they never married?

Ask your father/mother if he/she knows where and approximately when the grandparents married. With this information, you can ask for a search and ...

When a man naturalized before the 1922 Cable Act, his wife automatically naturalized with him, making her a US citizen involuntarily. That is why no naturalization records will be found for a woman in that situation. I’m guessing the Italian courts still insist on a “no record found.”

I know the ...

Registering minor children in AIRE is a simple process, so if your children are minors and will be for a while, there is no need to include them in your case especially if it involves more paperwork or greater cost.

The pre-1912 naturalization ended Italian citizenship for all members of the family, even those born in a jus soli nation before the naturalization.

Some have gotten around this by claiming citizenship through the mother, who was naturalized involuntarily, but that approach also requires a 1948 ...

Ok. An extra headache, but it will ultimately work out.

Great news. Congratulations! Did it work for your daughter too?

Again from Ancestry:

Michael Rose

Spouse Mary Ellsworth
Father Francesco Rosa
Children Charles "Charley"
Birth Apr 1867 Cercemaggiore, Campobasso, Molise, Italy
Death 7 May 1943 Chester Township, Delaware, Pennsylvania, USA
Residence 1 June 1915 Haverstraw, Rockland, New York, USA

I will check ...

You should also note that Antenati has posted the birth records from Cercemaggiore. I checked for Michele Rosa for the years 1866, 1867, and 1868, but his birth record does not appear. There are several Rosa’s but none for Michele. It is likely, if the date is correct, that he was born in a nearby ...

Also the odds are that Michele’s mother was named Lena (Maddelena). Note that the second female child was named Clara (for Clarissa, Mary Ellsworth’s mother). The first female child would have been named for Michele’s mother.

That would mean the 1864 birth I noted above is not accurate.

From Ancestry more detail on residences - Note that father is Francesco

Michael Rose
1867 - May 7, 1943
Spouse Mary Elsworth
FatherFrancesco Rosa
Born Italy
Died Chester, Delaware, Pennsylvania, USA
Residence
Elkland, Tioga, Pennsylvania, USA
Hide all residences
Trenton, Mercer, New Jersey, USA ...

This is another naturalization possibility

Name Michael Rose
Sex Male
Naturalization Date 4 Nov 1892
Naturalization Place New Jersey, United States
Naturalization Place (Original) New Jersesy
Birthplace Italy
Event Type Naturalization


I believe this was a county naturalization if you are ...

There is also a 1910 census for the family of Michael Rose (born in Italy and naturalized)
His wife, Mary, and children (Charles, James, Lena, and Clara) were all born in Pennsylvania

This is a possibility: birth date is off by 3 years but father (Francesco) is correct.

Name Michele Rosa
Sex ...

Maybe?

Detail Source
Name: Michele Rosa
Record Type: Naturalization Declaration
Birth Place: Italy
Declaration Date: 12 Jun 1889
Declaration Place: Pittsburgh, Pennsylvania, USA
Naturalization Place: Pennsylvania, USA