Just a few thoughts, since I'm sure others will chime in.
First, if you want to have a single 'incarnation' of a given element in your model, you have to live with the fact that a change to that single element will be reflected elsewhere. After all, you've changed it.
But, you can have divide your efforts into phases, such as analysis and design (you can get much finer-grained than that, but you get the idea here I'm sure).
If you want to keep your analysis work separate from later phases (perhaps second-stage analysis in your case), then separate these into (say) a separate view (a package immediately underneath the model root node) The view itself can have structure, including a package hierarchy, so you can set up an entire 'ecosystem' of domain models, or whatever.
When you move to a later stage, do the same thing again. Make new packages and entities in the new phase. You can always start with copies of entities from earlier phases - you'll see why in a moment.
You can now create «trace» relationships between relevant items (at the element or package level) between the phases, so that your audience can trace late-stage entities back to their antecedents in earlier phases.
Now you can modify an entity in either phase, without breaking it elsewhere.
You're still left with the issue of having a modification ripple out across a given phase. This should not be an issue. If other diagrams (for example) are meant reflect the same element, then you should see changes in all cases. If the other diagrams are reflecting something else that looks similar to your original, then make the other instances separate entities, specifically so that changes won't ripple through unrelated entities.
Consider things like inheritance, or perhaps an object model. Often when you are having this sort of quandary it is a sign that you need to be working with a different diagram type.
Hope this gets you started,
David