Seems to me that its really just a question of using CDs. Really this could be a pretty late change, based on your POD I'd have to assume that it would be a crash program based on Sony's initial success. Something involving buying and integrating component from the CD-i or 3DO could fit the bill (both a big stretch in terms of corporate culture, but there are some interesting possibilities there), but realistically there wouldn't be THAT dramatic a hardware change in switching the N64, and 2 years would probably be enough to get something together in house. A very early DVD implementation is also possible, but probably not without delaying the launch to at least Christmas 97 and still requiring Panasonic cooperation.
All in all the most likely scenario would probably be Nintendo simply reacting to the surprisingly robust PlayStation launch by switching the N64 to using CDs, developing it internally and getting the box out for Christmas 1996 as OTL. This is possibly stretching likelihood, but is certainly possible. If they are aggressive about porting PlayStation titles and ease up on developers they could pull ahead very quickly with all the momentum from the SNES era, though more likley IMO Nintendo's restrictiveness on devs (though definitely lightened from the NES era) will mean that the PlayStation still gets considerably more titles overall, and that while Nintendo finishes ahead it won't be by all that much, and "victory" won't be all that clear until the end of the cycle when the N64's hardware advantages can be best brought to bear. If, as is more likely the revised N64 gets delayed until 1997 I have a feeling they wouldn't be able to make up the lost time, and will be harmed even further by delaying the replacement in the hope that the N64 will be able to compete with the PS2 (you might even see the 64DD being a DVD expansion, but it would probably have about the same impact it did OTL).
Nintendo being what they are however I have a hard time seeing any of this. Most likely would be that the N64 releases as is, and is followed by a CD expansion in the vein of the original Sony/Nintendo cooperative PlayStation for the SNES. It would probably have some impressive titles, especially first party (and when combined with the memory expansion), but we all know how things go with console expansions.
I don't know how well it would end up placing Nintendo realistically, but my inclination in terms of writing a timeline (speaking more in terms of storytelling that works and is plausible than most likely outcome) would be to have Nintendo get involved in the 3DO console after the Sony deal falls apart, certainly releasing a 3DO expansion for the SNES and significantly changing the face of the project (I'm thinking perhaps something along the lines of allowing other companies to produce CD only devices but going to some lengths to give advantages to the in house, cartridge capable, SNES-CD systems). The follow up would be an all Nintendo, possibly DVD based, Nintendo 64 released as a contemporary of the Dreamcast. The biggest problem here is ultimately that Nintendo would very likely get a reputation for expensive consoles (the exact opposite of how they have traditionally operated), but I think they might be surprised how far they could get by reducing software prices (though how far they would, with a likely even more significant than OTL loss on the hardware is a big question). That said, the big advantage they'd find is that a somewhat upgraded N64 with DVDs released around 1998 could be competitive well into the Xbox era, so the end result might be that while not maintaining the clear dominance of earlier generations they also don't get OTL's reputation for technologically limited systems (having none of the bottlenecks all of N64, GameCube and Wii got saddled with) and breaking down the clear five year console generation cycles much earlier than OTL.