Actually no, dilution doesn't really extend open time. In fact oddly, diluting a glue can make it go off faster because water evaporates (or is absorbed by the substrate) faster from a fluid mixture than from a more viscous one, and by their nature more watery mixtures tend to sit more thinly on the surface to begin with.
Franklin (makers of Titebond) used to say in their FAQ for Titebond1 that they can be safely diluted by only 5%. From experience in related areas I expect this to be conservative, but rather than face a glue-line failure it's probably best to treat this as gospel.
If you need a much greater open time than that provided by a given PVA it's better to look into using a different adhesive. Epoxy and foaming polyurethane are two of the commonest choices, room-temperature hide glue and urea-formaldehyde are also good alternatives for specific applications. Note however that clamping needs for each of these glues is not quite the same as with PVA, so some adjustment in your procedures may be needed to get the strongest joints possible2.
1 This information appears to no longer be given on their website.
2 Epoxy for example is one adhesive where it is possible to starve a joint with high clamp pressure (something that is essentially impossible with PVAs, despite the widespread belief among woodworkers to the contrary).