Hello and welcome to bitcointalk.
It is impossible to invest in an exchange unless you are close to the owners.
All the major exchanges that I know don't have any investment system, but all I can offer you is to try to contact them via the ticketing system/email.
If you have a large amount of money to invest, they may consider that.
I would suggest you to search for a small exchange, as the big exchanges have already done big profit and will probably won't be interested in any more funds( they won't need anymore funds as they already have enough to maintain the site.)
but some people are still hesitant to invest in exchange that is still the age of corn
averagely, their customer support / ticketing support is very long to respond to questions. and also the biggest risk is scam, there is no money back guaranteed to our money.
but maybe it's worth considering, due that new exchanger is still quite need some investors