Complete copy of a handle class-based architecture

Hello,

I do have a handle class-based system archtiecture with internal links of objects (the architecure represents a component-based pyhsical model). Each architecute can be individually assembeled and internally cross-linked. Although it is much more complex, for this question, it can be seen similar to the Matlab Doubly Linked List object. At the end of an assembly I would have a single object which represents a complete system (incl. many linked objects):

architectureObj = classSystem();

As typical in physical applications the system needs to be applied to different scenarios (with different values, e.g. Temperature), however, the architecture stays unchanged.

scneario_1 = architectureObj:
scenario_2 = architectureObj;

Now, there is the problem that it is not possible to treat the architectureObj as value class with different values for each scenario. Since I need the handle class features for the assembly process I could not change to value classes. I would more need a deep copy of the complete assembled architecure including copies of all internal connections without destropying them. Is this somehow possible? Do I have to rethink the concept?

Thanks in advance!