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).