That is, if one drywall anchor supports 50 lb, will two support 100 lb? Four support 200 lb? etc.
Drywall – Does the supported weight of drywall anchors scale linearly
drywall-anchor
Related Solutions
I almost always use the self-drilling stud solver type anchors. I find that they are tough enough to hang just about anything.
Aside from those, the only other anchors I've found that I like are the toggle-bolt type, which are more useful if you need to hang something from the ceiling.
While having all four mount points connect to structure (aka: the stud) is ideal, I think in your case, having two mount points in wood and two in a drywall anchor, you're going to be ok.
Consider this question: What is the weight capacity of a drywall screw?
One drywall screw CAN (not should) hold a lot of weight for its size. Also a properly installed drywall anchor can typically stand 70~ pounds of pull force (as in pulling out, not down).
With two WOOD (not drywall - wood) screws set into the available stud and 2 (or better, 4) drywall anchors, I think you're not likely to exceed the capacity. If your cabinet total weight when full is < 100 lbs you're probably not going to have a problem.
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Best Answer
This should largely be the case as long as the anchors are relatively far apart.
Think of it this way, two 50lbs. anchors on different walls can each support 50lbs, whether or not the load(s) supported is shared between the two or not.
However, any holes in the drywall weaken it slightly, so while an anchor in drywall may be rated for 50lbs, putting two within a few inches of each other will decrease this rating.
I don't have a good answer for how far apart the anchors need to be, but if you can span anchors to 16" apart, you might as well just mount directly into the studs (assuming 16" OC).