Macro to Copy Rows to new sheet based on Multiple Criteria

I've been searching the forums and there are many answers that get me really close to what I need to do: I need a macro that copies entire rows of information based on multiple criteria being True. I have attached a simplified version of the spreadsheet, and I'd like to be able to run a macro which populates the sheet labeled as ACME with all rows the have an open Issue (Column F) AND have ACME as the responsible party (Column H) OR the Support (Column I).

What would be really nice, but not necessary at this point, would be if a dialogue box popped up asking which company you'd like to search for open issues with, but for now, I can just use multiple macros to pull information for each company.

There are some pretty fantastic answers out there, but for the most part, they're just addressing moving information based on one-criteria. The and/or is really throwing me.

Quick question, how about strings like "Eleven/Acme" and "Acme/L. Sklar" should these be excluded or not?

Alf