For example, your app icon would be blue and black and your logo on printed shirts would be red and black.
I'd avoid this at all costs.
You want your company to be as rememberable as possible so consistency and repetition is key. People recognize andr remember patterns so use this to your advantage. You need to keep a consistent visual language across all touch points so people remember you and associate a look and feel to your company and your product.
I'd pick one and stick with it - and if you aren't sure which one to select, do some split testing to check performance.
I hope this helps,