Get the max current through relay without activating it
You can try to very slowly ramp up the current to slightly increase the 12mA, but no matter what you're doing: 

Your relay is an electromagnet, and the force an electromagnet can exert is directly proportional to the current through it. 

So, there's no reliable way to drawing significant current through your relay's coil without risking to trigger it – after all, any relay is designed to reliably trigger.

I sense a very strong XY Problem here: you're trying to solve another technical challenge by trying to pull current through your relay. That's almost certainly the wrong approach, but we can't help you find the right approach without you telling us what you're actually trying to solve. So, I recommend editing your question and telling us exactly what you're trying to solve, and why the relay coil has to be in line in your application.