I have the DNA splicerS (see the emphasis on the s?). I have both black 1 and 2, traded over my original kyurem and reshiram hoping to be able to have both black and white kyurems in my party but it will only let me have one. That's a downer as having both was a big reason why I got the game (other than it being pokemon). So am I doing it wrong or is there some little exploit I can do to make it work.
The Splicers' effects (there are two pins according to the description) are Links to Kyurem to allow him to Absofuse with Zekrom OR Reshiram. Once you fuse, the pins' effect changes to separate the fusion.
Since in their world only 1 Kyurem, 1 Reshiram, and 1 Zekrom exists at a time, only two of them can fuse at once. This has been answered, next time use Q&A.