Things I would think about:

• Connecting it to myself - its easier to care if it's yours or you have ownership about a thing. (obvious example - having your own children, or treating it like they are children/related to you, but this also applies to things and not just relatives. For example I have built some of my furniture from scratch which makes me particularly like those possessions over purchased ones.)
• following on from that last point; spending a lot of money on the thing, can signal to yourself that you care about it (i.e an engagement ring).
• I particularly concern myself with caring about seeing fairness in the world; I like to believe I am one of those people who would stop the injustice from happening in front of me on the train. Because of this - if I could find a way to connect caring about the next X more salient to the goal of "protect justice" which is something I already believe in, doing so would help.
• Having evidence that you might prove this empirically. How might you know that someone else is protecting something? Are there things you can do to signal that? (signalling this would likely cause you to feel it more for yourself as well)

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