LEDs only change their voltage a little bit when you increase the current.
First you need to know how much current your LEDs can take in the long term. You can really only be sure by looking at their spec sheet. Power LEDs you can easily overdrive by 2x, 10x, and they'll last for hours, days, or longer but slowly degrade over that time. What I'm saying is it's hard to find out what they can take by experimenting with them.
As far as the resistor value goes, unless you have a specifications to show how much the LED voltage changes with a change in current, just start by assuming it won't change. So if you halve the resistor value, the LED current will double. In reality, the LED voltage will go up some, lowering the current a bit below that prediction. The intensity of that effect on the new current will vary depending on how much of the source voltage was dropped across the resistors to begin with.