The human eye can see in UV—if the lens is removed:
You may have heard that digital cameras can be made sensitive to infrared light by removing the IR filter found inside, but did you now that something similar can be done with the human eye? People who have aphakia, or the absence of the lens on the eye, have reported the ability to see ultraviolet wavelengths. Claude Monet was one such person.
The Human Eye Can See in Ultraviolet When the Lens is Removed
However, without the lens, the eyes are more vulnerable to UV damage.
I see no reason why eye size can't be increased to three times the current size, although you'll need to also modify the skull so that it all fits. (Obviously this is not a change you can make to living humans.)
Some primates have very large eyes compared to the size of their body. It's actually a little unsettling:
Tarsiers - The Big-Eyed, Ancient, Nocturnal Mammal
360 degree vision
There's a big difference between dragonflies and humans here due to the placement of the eyes:
Eyes that face forward on a skull suggest a predator. Forward facing eyes allow for binocular or stereoscopic vision, which allows an animal to see and judge depth. Predators need this depth perception to track and pursue prey. Cats and owls are excellent examples of predators that use forward facing eyes when hunting their prey. Monkeys also have forward facing eyes that give them depth perception needed to swing and leap in their tree top habitat. Humans have forward facing eyes as well.
Animals with eyes that are located on the side of its head would suggest a prey animal. Side eye placement allows for greater peripheral or side vision. This enables the animal to see predators approaching from the side as well as from behind. This vision is very important for protecting an animal when it is grazing or feeding.
How to "Read" a Skull: Eye Placement and Size
Even with larger eyes, vision will not be 360 degrees. The skull would need to be significantly redesigned so that the eyes are on the sides of the head, not the front, but even this will probably have blind spots in front of and behind the head.
You don't actually need to make any modifications to the eye to get the effects you want. The solution is quite mundane actually: all you need is VR goggles and a camera that sees in 360 video and UV. Each eye gets a fisheye image that shows UV light. Of course, training will be needed so this isn't super nauseating and confusing, but I think it's possible for the human brain to adapt (since our brains are very adaptable).