Grafting Compatibility

This can be one of the more confusing parts about grafting.  I will try to provide some information here, but while there is some black and white to it (e.g. you can not put an orange on an apple and vice-versa), there are also many of shades of gray. 

The California Master Gardener Handbook contains a helpful chart presenting the general compatibility rules applicable to common deciduous trees.

When reviewing the chart, pay close attention to all of the footnotes included with it.  Note that the chart presents the compatibility of fruit types with specific fruit tree rootstocks.  With most home grafting, keep in mind that the scion wood is usually not directly grafted onto the fruit tree's rootstock, but rather onto another variety (or interstem) that was grafted onto the rootstock.

Here is a general guide and a caveat example adapted from the information in the chart:

Grafting different varieties of the same fruit type onto the tree with that fruit type normally should work. For example, grafting a Fuji apple onto a Gravenstein apple tree or vice verse is doable.  Similarly, grafting a Satsuma (Asian) Plum onto a Santa Rosa (Asian) Plum or vice verse can work.  While grafting Satsuma (Asian) Plum onto a Bavay Green Gage (European) Plum can work, the opposite approach will fail.  You can not graft Bavay Green Gage (or other European) Plum onto a Satsuma (or other Asian) Plum.