I'd be cautious about upping the amperage of the fuse too much. If the body of that splitter is all plastic and the wire is fairly small (18 awg or smaller), then it probably is designed to carry minimal current which explains the 2 amp fuse.
I have a splitter here that has one of the three outlets made of all metal and ceramic materials. And it has 14 awg wire and a heavy duty male plug. That suggests that the splitter can safely handle higher current loads, possibly even a lighter, up to the rating of the vehicles outlet. Another one here is all plastic and has 16 awg wire. I don't run anything too powerful through that one but it works just fine.
My truck has a 20 amp auxilary outlet which could easily fry a light duty splitter if not properly fused.
Test the splitter with a 2 amp fuse and your favorite accessories. If the fuse holds up, you may be good to go as is. If the devices tend to blow the fuse from time to time but not often, you are probably right on the edge. Going to 3 amp is likely not a problem, but I would be leary of going any further.
Hope this helps.
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