I want to create my own deb repository to store some packages. I've tried
reprepro and it works fine, except for one fundamental feature. Reprepro can't
store several versions of the same package in the repository.

The ability to store several versions of the same package is essential to
me, so I'm asking what software can can do this.

Here is a piece of reprepro FAQ that shows that it can't do it:

3.1) Can I have two versions of a package in the same distribution?

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Sorry, this is not possible right now, as reprepro heavily optimizes

at only having one version of a package in a suite-type-component-architecture

quadruple.

You can have different versions in different architectures and/or components

within the same suite. (Even different versions of a architecture all package

in different architectures of the same suite). But within the same

architecture and the same component of a distribution it is not possible.