I've been thinking about something like this for a lot of years.  Conjugate programming worked really well for my bench press especially.  My squat went up about 100lbs at Westside.  My deadlift went up 30lbs.  BUT, my bench press went up over 200lbs and my body weight didn't fluctuate that much.

One of the most important parts of my time at Westside, which was only around 4 years, was the first 6-8 months of Louie having me do bodybuilding work.  We did a lot of anterior work, such as fly's, elbows out DB presses, a ton of weighted push ups, and machine bench.  This machine never gets talked about in articles, but was a major component of Westside training, even George Halbert used it with 14 bands wrapped around the back of it.

After the 4 years at Westside, I had a massive stroke in 2010.  I then decided to go raw in 2013.  I tried to jump back into Westside training and really got nowhere with it.  So, I jumped into 5th Set and the thing about it that i had never paid attention to was periodization of accessory work.  During this time, I had to relearn how to lift weights from geared to raw, which uses different technique and muscles.  Shout out to Brandon Lilly, Matt Wenning, Glenn Baggett, and all the others who went from multi-ply to raw.

What I tried to do for this program was use periodization or "Waves".  I use 3 week waves, which is more akin to what I trained at Westside, which is why I think we saw the vast improvement in my bench.  I did 5x5 instead of 8x3, and I saw the most significant increase of my bench while I was there.  That was a period of time where I had an 800lb bench press and my anterior delts and pecs were the biggest they've ever been.  

So, when I began my 5th Set journey, my raw bench went from 490 to 580lbs in 2 years.  The biggest difference was the amount of volume and accessories.  I believe you need more work in your anterior chain than is used in a traditional Westside training program.  Chest work, pec work, delt work, but also tricep and back work too.  

I've also given you waves of different bars, bands and chains, and a straight bar.  I would use the last week of this training, as a one board press or something like that as an indicator of improvement.  While I was at Westside, that is how I indicated one rep maxes.  

Doing this program, I would advise you already have a strong base.  Bench press should be at least 350lbs for men, and 165lbs for women.  You'll also need to have a reasonable understanding of your body, the gym environment and equipment.  Highly recommended training in groups or with a training partner.  This was an essential part of the Westside mentality.