Mulligans from Bailieborough

My gr. grandmother was Margaret Anne Mulligan, est birth 1868. Emigrated to San Francisco, California around 1888. She passed away on March 21, 1947. 

This is what I do know about her Margaret and her family in Ireland.

She had four brothers, John, James, Owen and Patrick. I have found information about Patrick est. birth 1867, he left Ireland at some point (possibly with Margaret). He passed away in Aug 1901 in Auburn, California and was buried in San Francisco.

According to his obit, he was born in Bailieborough but that is pretty much all the information I have. 

I don't know the names of their parents, or even exactly where or when they were born. I am pretty certain it was in Cavan. 

I don't know if the other brothers left Ireland or stayed.  

Another name that has been mentioned in family lore is Termon An Tearmann in Donegal. This has been mentioned as a possible birth place for Margaret as well. 

I have an ancestry account, and have been conducting genealogy searches on numerous sites and for quite a while now. I also have been anaylizing my DNA matches but yet, the Mulligan family has proven to be the most challenging to find information about. 

If anyone has any tips, or information, or oral history about the Mulligan Family in this area, that would be amazing! 

We have been able to connect with relatives in other parts of Ireland from different family lines through genealogical research so finding this connection, or really any solid information, would be fantastic.