Images in the 1-0 S(1) line of molecular hydrogen at 2.12 mu m of six extremely young stellar objects are presented: NGC 1333 IRAS 2 and 4, L1551 IRS 5 and NE, L1634, and IRAS 08076-3556. In an cases, we find H-2 1-0 S(1) line emission from bipolar jets of various degrees of collimation. In two sources (L1634 and IRAS 08076-3556), morphological arguments strongly suggest that previously made identifications of the outflow source with near-infrared sources have to be revised. In L1634 we find evidence for a second, previously undetected outflow. IRAS 08076-3556 may also have a second outflow, although our data are less conclusive. The outflow in L1551 NE and the double outflow associated with NGC 1333 IRAS 2 are confirmed by our imaging data. Multiple outflow activity is seen toward all of the regions imaged here. We speculate that the formation of small groups of stars within one outlfow lifetime is a rather common occurrence.