It’s not very obvious in LinkedIn how to search within a particular person’s connections, and particularly how to use advanced search features there, but it’s possible. I had to figure out a URL “hack” to do advanced search within all contacts without narrowing by keywords. Here’s how:

1. Go to the person’s profile.
2. Click on their number of connections (e.g. “500+”).
3. In the top right of the “Connections” panel, click the gray magnifier.
4. Type “a” (or anything that gets you at least one result) into the search field.
5. Click the “advanced search” link to the right of the number of results, below the “Connections” panel heading.
6. In your browser URL bar, delete the search keyword (e.g., “a”) between “?keywords=” and “&pivotType”.

Here’s an example of an initial page URL with “a” as the search keyword. (If you want it to actaully work, replace 1234567 with the profile ID of one of your LinkedIn connections):

https://www.linkedin.com/vsearch/p?keywords=a&pivotType=cofc&pid=1234567&trk=prof-connections-search-advanced

If you edit out the “a” after “?keywords=” you can then use the advanced filters (e.g. location, company, industry) within all of the person’s connections:

https://www.linkedin.com/vsearch/p?keywords=&pivotType=cofc&pid=1234567&trk=prof-connections-search-advanced

To search using keywords and advanced search filters, just redo step 4 with the keyword(s) you want.