How to find Second Mode across various columns

Hi,

I am having a difficult time trying to find a way to write a formula that would essentially give me the 2nd mode across a range of columns that actually skips columns in between.

For example: my current mode formula looks like this:
=MODE(F2,I2,L2,O2,R2)

As you can tell, this is not a consecutive range, and the mode is basically derived from every 3rd column in between F2 and R2.

What I can't figure out is how to create a 2nd mode, or a 3rd mode for that matter.

Sufficed to say, I would definitely appreciate any help/insights offered.
I've also attached a sample file if it helps.

Thanks in advance!