I have compiled a body of work from numerous contributors, who all licensed their individual works to me under CC-BY-SA version 3.
Can I now instead redistribute their work under CC-BY-SA version 4?
I don't think so, no. CC-BY-SA 3.0 allows in s4 that
You may Distribute or Publicly Perform the Work only under the terms of this License ... This Section ... applies to the Work as incorporated in a Collection
You may Distribute or Publicly Perform an Adaptation only under the terms of: (i) this License; (ii) a later version of this License with the same License Elements as this License; ...
That is to say, if you were to redistribute each of these works verbatim, individually, you would have to do so under CC-BY-SA-3.0; the permission to uprate the license to (eg) CC-BY-SA-4.0 applies only to adaptations.
One might argue that the mere act of collecting the works together constituted adaptation, but CC-BY-SA-3.0 is pretty clear above that the people who wrote the licence didn't think so. In one of the few pieces of jurisprudence we have on CC-BY-SA interpretation, Drauglis v. Kappa Map Group, the judge held that placing a CC-BY-SA photo amongst other photos on the cover of a road atlas didn't make either the entire cover or the entire atlas a derivative work of one of those photos, which again to me argues that mere collection doesn't make an adaptation.
Based on my reading of the CC-BY-SA 3.0 license, it is OK to change the license of the Collection but not to change the license of the individual works that comprise the Collection.
We have two things to be concerned with, the Collection and the Work, both of which are defined in the CC-BY-SA 3.0 license.
Sections 4(a), 4(c), and 4(d) are the relevant sections for dealing with works that are licensed under CC-BY-SA 3.0 and collections. What follows is my understanding based on reading those sections.
First, you own the collection. You can release the collection under any license that you choose. There are requirements in the CC-BY-SA 3.0 license about how you provide attribution to the creators of the individual works that are part of the collection, but also give the creator of the individual work the ability to request the removal of credit. Section 4(d) does place some restrictions that the creator of the Collection "must not distort, mutilate, modify or take other derogatory action in relation to the Work which would be prejudicial to the Original Author's honor or reputation" unless such things are permitted by applicable law.
However, you do not own the individual works. Unless you take action to change the license, those individual works will always remain under CC-BY-SA 3.0.
From a practical perspective, it doesn't make sense to release the collection under a more restrictive license than CC-BY-SA 3.0, though. If all of the works were licensed under CC-BY-SA 3.0, then anyone who receives the collection also receives a license to the individual works under CC-BY-SA 3.0 and can use the license to make a collection from those works and release it under a less restrictive license again.