Two health insurance policies?

petersprojection

Hi all,
I have been looking at private health insurance policies and haven't found one that I'm satisfied covers everything, without some limitations that concern me. I am self employed in a physical job and my health is obviously important. I'm not so concerned about the premium as having the confidence that if I need something, then it will be covered. 
I have had cover with a company for some years. Their premium is very high and they do not offer the coverage of some of the other providers but I do prefer some of what they offer. I am in my 40's, healthy and have never made a claim. I do not however feel like a 20 y/o anymore and imagine I'll need some help to keep going before my retirement!
The most important thing to me is to know that if I need it, it is there, without finding out that whilst I'm covered for many things, it's only up to £500 etc. or that whilst I'm covered for one thing, not for others.
I have been considering taking on an additional policy to cover the shortfalls in the current policy. However, there would be some overlap. I'm not looking for cash benefits from both companies or anything like that, if I was covered for something by the original insurer I would likely claim from them as that would seem fair, but if they didn't cover me for something I would be able to claim from the new insurer?

I can imagine that the answers will go one of three ways - not allowed, it's too messy or yes and claim from which you like. I'm hoping for the latter but will wait for your responses with interest.

Thank you in advance,

Peter.

petersprojection

Does anyone have any knowledge in this field?
Thank you.