The general answer here is "capital stack". The more versatile and available your capital stack the better off you'll be trying to navigate similar situations. It's hard to really summarize all the ins and outs of capital stack, but it essentially refers to the different types of debt and equity you have available to you.
Using the example above. You need to find an extra $120,000. Let's say you get a private unsecured loan from your rich aunt. Now you have $100,000 left. Maybe you get someone to come in as a preferred equity partner. You'd be paying them a preferred return and then have some sort of pre set agreement as an "exit fee". The exit fee could be if you sell it they get X% of the profit, if you cash out refi, they get a flat exit fee once that happens. That's just one example of how a capital stack can look.
Ideally you want to keep your capital as simple as possible. 100% financing for this would be the simplest and easiest. But having the availability of a diverse capital stack can mean the difference between making a deal happen and not. The more lenders and investors you start to work with, the more people you'll be able to call up and see if they are interested. Some larger commercial brokers can also help you place equity, but that's typically for much larger deals.