Find unique matches for multiple criteria within a row of cells

I have a single large (~400k) row of job titles and I need to find the unique number of matches for multiple "contain" queries.
Example, for the row below:

Director IT
VP Sales
VP Operations
Technology Analyst
Database Manager
Compliance Analyst
Director of Security
Chief Technology Officer
Chief Information Security Officer

I ran two COUNTIFs-
1. COUNTIF(A:A,"*technology*"), which returns 2 matches.
2. COUNTIF(A:A,"*officer*"), which returns 2 matches.

The problem is I need UNIQUE matches of these 2 (and many more criteria). So I need to somehow combine the 2 formulas above to return only unique results, which in this example would be 2 (there is one record with both "officer" and "technology", which I do not want to count twice).

Any ideas? (besides buying Access)
Thanks in advance!