Multiple entry visa for British citizen?

Hi, I was hoping to obtain the six month multiple entry visa in china for next May but upon further reading this doesn't seem possible. A lot of information is conflicting so I would just like to check to see if my proposed itinerary for next year is possible.

1. Fly from London to Shanghai beginning of May, I will have a ongoing flight from Shanghai to Melbourne end of September but will not be in China for the whole time, hence the multiple entry.

2. Travel from Shanghai to Beijing overland to get a return train to Mongolia, return to China to visit friends who live there and also do some unpaid voluntary work for a charity. I will be in China for 2 months.

3. Return flight from China (cheapest airport/flight) to Nepal so one month in Nepal to return to Shanghai to get my onward flight. This in country time will be less than a transit so that may be an option.

A multiple entry would work as I can split my 2 months up with a visit to Nepal, if they are being issued?
I then thought about getting separate ones but if I were to travel to Mongolia it seems near impossible to obtain it without a letter of invitation.

Can anyone tell me if this route is do-able? It is very confusing.

Thanks so much for any information that anyone can give me in advance, apologies for the length.
Natalie