Oh yes, I've searched on only given names such as just "Matteo" aged 0-2 years old (YOB 1885 or 1886) during the time period, I've searched on just "Francesco" ( YOB ~1861 the father) but that is like searching on "John" and unfortunately the most unusual first name "Wilhelmina" (YOB 1863 the mother) does not show up at all and I've tried all the various Italian or French spellings of that name (Filomena, Philomena, Guglielma etc). I have a feeling she may have used one of her other given names, though I do not know what they are. I know her siblings had multiple given names so it is safe to presume she did as well.
I have not tried transposing the family name (Soncini) for the given names or the mother's maiden name (Mori) either. I'll try that next.
I've found the SteveMorse search engine helpful and it narrowed down the number of ships whose manifests I must page through to about 75 ships...so that is where I am now.
I've asked for a document from New Jersey that I hope shows Wilhelmina's other or original name(s)as it was created very shortly after they were to have arrived in the USA. Hopefully I'll know more in a few weeks.
Thanks for the suggestions.