This is quite possible to do, however it requires quite a bit of HTML and CSS experience to achieve as you can do it using the Bootstrap modal.
Bootstrap is including with Toolset so you can go to Toolset -> Settings and scroll to bootstrap loading to enable bootstrap.
Then you can use the examples below to setup your modal. hidden link
It should be noted that this cannot be achieved using the Views Block editor and you will need to enable the Classic editor for your archive by going to Toolset -> Settings -> Editing experience and select the 3rd options. Once you've done this you should see the option for the archive editor appearing.
From there you can now create your Archive using the classic editor and make use of the Bootstrap html and css to setup your modal. You will need to design your modal to load whatever post data that you want as it won't automatically load the information from the post.
Using the Fields and Views buttons on the Archive you should be able to add the items that you want to your modal.
