If there is a will there is a way. But I would say that the mower has been designed that way for a reason. For example, if you have more weight on the back, it will make the front lighter which would make you unknowingly lift the front of the mower up every time you take a step. Also the extra weight put on the bag mounting points could be a concern. If it was possible , the lawnmower manufacturer would have likely had it as a purchasing option so they could make more money.... but needless to say of course you can make one, it may just take some creativity.
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Have you considered switching to a mulching blade? No bag to empty and the clippings decompose and fertilize your lawn. I realize this is impractical if you have really long, thick grass. At our old house we only bagged during peak growing season and have never bagged at this one.
Can you post a photo of the mower?
A lot depends on what you have got - Bigger weighs more.