We present evidence that the luminous infrared galaxy II Zw 96 (log(L-IR/L.)=11.89) is a merger containing powerful, young starburst regions, similar to VV 114 and the well-studied Arp 299 system. Our analysis is based on spatially resolved K-band spectroscopy and new optical and high-resolution near-infrared images. Four primary infrared sources are found. One (source A) may be a galaxy nucleus, since it shows morphological hints of a stellar bar, and is in the threes of powerful starburst activity. Another (B) seems to be a relatively quiescent spiral galaxy. The remaining two sources (C and D) are very red with strong near-infrared emission lines from atomic and molecular hydrogen and helium. They do not seem identifiable as galaxy nuclei, based on morphological grounds. Therefore, they are most likely highly obscured, luminous (M-K similar to-21) starburst regions. Comparison of the near-infrared spectroscopic diagnostics of sources A, C, and D with starburst models suggests that these starbursts are younger than those in most other infrared-luminous galaxies. We note both qualitative and quantitative similarities between regions A, C, and D and ones in the interacting galaxies Arp 299 and VV 114. We suggest that these three systems are in a similar evolutionary stage, containing very young starbursts and seen before the final dissipative collapse and dynamical relaxation which numerical simulations predict for major mergers. If this analogy is correct, the starburst regions are probably groups of the super star clusters, rich in OB stars, which are ubiquitous in starburst galaxies. An important, yet open, question is whether these galaxies represent part of an evolutionary sequence, a stage through which most or even all infrared-luminous mergers will pass. (C) 1997 American Astronomical Society.