Filter for string in multiple columns

Hello there, new member, and I have a dilemma I hope someone can help me with.

I am staffing an upcoming event with volunteers and I want to be able to a single volunteer across their various shifts and locations. However, I cannot guarantee that a particular volunteer will always be in the same column on my spreadsheet so AutoFilter doesn't do the trick. I've tried using Advanced Filter options as well, but I either can't seem to get it to work or it won't work with strings.

I've attached a sample of the type of document I'm working in (genericized) so hopefully my below questions will make more sense.

Ideally, I'd like to be able to be able to search/filter for Joe and see rows 2 and 3 appear. Is this possible?

Additionally, I'd like to know who is also on shift together. For example, is there a way to search for Tony and Sarah together and have row 5 appear. I know that I can do this now with filtering column 2 and then 3, but the real document I'm using is over 800 rows long (very big event!) and using progressive filtering would take longer than I'd like.

I hope what I'm asking makes sense and is not sounding too crazy! Please let me know if you have any suggestions or need more information.

Thank you in advance for your help!

Hi FDibbins, thanks for the quick reply and welcome!

I thought about using a helper column, but I would need one for each of my volunteers, right? Unfortunately, I have over 50!

The second formula you provide looks interesting. I haven't tried it, but it would recalculate the 1s in that column based on what name I entered into the top cell, right? That sounds more doable, but still time consuming. Is there any way that might not requie a helper column?