These surfaces are very similar to the Type (+-+|-) surfaces (after all, we just change a sign…). The added horizontal handles are just shifted a little.
The divisor of the squared Gauss map is shown below. Here, the parameters satisfy a+c+d=b+1/2.
For fixed τ, one has a 1-parameter family that connects to (possibly equal) noded limit with sheets parallel to the xz- and yz-planes, respectively.
Again there is a more symmetric subfamily with horizontal straight lines. We see here that in contrast to Type (+-+|-), the normal rotates along these lines. It is not clear that these two types can be deformed into each other as minimal surfaces (after relaxing the symmetry conditions further).
Resources
PoVRay Sources
Minimal Surfaces 