2 different passports, 2 different visas

[Merdo123]

Hello everyone,

I am a self employed UK resident with a Turkish Businessperson Visa. I have been granted leave to remain since June, 2017. I need to renew my application every 3 years. My business requires me to travel abroad very often since it is an international business. However the visa renewals take 6 months and in this while my passport has to stay in the Home Office. Hence, I can not leave the UK and this is completely destroying my business. Also, I am working as a dentist back in my country and also I am one of the shareholders of the dental centre in Turkey. This condition keeps me away from my profession.

I think I have found a solution for this but not sure if it will work. My solution is:
As the UK gives second passport to their citizens who needs to travel a lot, I can get a second passport from my country as well. And while my first passport is at the Home office for my Turkish Businessperson Visa extension, I want to apply for a different visa(?) with my second passport.

The problem here is, I am not sure if I can apply for a different visa with my second passport while I am waiting for my Turkish Businessperson visa. If it is possible, for what type of visas I can apply?

I am looking forward to hear your suggestions.