The first thing to notice that this isn’t going to be a “complete” burr, there is no final key piece that you could just slide in to lock the puzzle. This means that there will be empty spaces inside the solved burr, so it’s quite likely that some of the pieces can move a bit without the burr coming apart.
Therefore, not only will you have to figure out the proper alignments and order of the pieces, you’ll have to find a way to wiggle the pieces to their interlocking configuration.
The surefire way to approach these puzzles is the systematical one. Give a name to each piece, develop some kind of notation for the position and orientation of each piece, and start to go through all the possible combinations in some order that goes through all the possibilities eventually.
This seems like quite a big task: there will be quite many possibilities. Most of them will prove impossible very early though, either by blocking another dimension’s pieces, or obviously leaving some of the slots visible in the completed burr.
The above filtering will exclude most of the possibilities even without checking more than the pairs of parallel pieces separately. If you are brave, you can even skip it in the beginning, and start from the next step.
The next step is to try to find a suitable combination of positions and orientations for the pieces. I find the best way is to build the horizontal pairs separately on a table, and the vertical one in hand. Then, only if the arrangement seems plausible, try to figure out how to actually put the pieces together. This is pretty much a trial and error thing for me; the only bit of system is the choice of the final piece to go in.
This should solve even the most difficult interlocking burr puzzles, but it can take quite a bit of time (a couple of hours) if the burr is very complex. Judging from the relatively simple shapes of the pieces in the picture, that one probably isn’t at the very deepest end of the complexity pool. Given that it’s “special edition”, it may even have so few options that it’s actually unsolvable. Proving unsolvability will be impossible without the systematic approach. (No cheating with computers allowed!)
Good luck, and remember to only touch 3 or more pieces together when you already have a solution in mind!