Hi Ikea,
I have found that they are self regulating,and all the fruits the plant sets will mature up great.... but at the end of the season,you will then want to reduce the fruits to an acceptable but limited number...

{{gwi:84468}}

{{gwi:84469}}

I let cantaloupes set on what they will...11 per plant seems about the limit with 4 or 5 more common.

Watermelons often [but not always] need some checking on as to how many fruits are set on at a time. Too many will usually hurt quality. I have 2 Orangeglos that have kept setting on more younguns and I have let them keep 5 between the two of them for now. I would rather have one excellent watermelon than 3 fair to poor ones. Vine strength and variety size will vary...small iceboxers can handle more at a time.

Gee, I wish I had this problem. So far with 4 different melon plants of the charantais type growing as a test, I have a single melon growing. And to add insult to injury, the vines are so tangled, I'm not even sure which one produced my lonely only melon!

Susan

If you're growing for competition, leave 1 melon on the vine.
How's your fertilizer situation? When the vines start to run it's time to fertilize with higher P and K values for flowering, fruiting, and roots. Too much N will give you lush foliage and little to no fruit.
I like to grow 2-3 melons per vine to maximize size. Pinch off all other female flowers.
If you want more melons, plant more seeds.