Need to combine vector layers, but not with merge (QGIS)

I have four overlapping vector layers. Each is a grid with a single field of interest: numpoints.
I want to create a single output layer that is a single grid, with a field sumpoints that is the sum of the numpoints field in each of the input grids.

The grids overlap, but not completely. I want the output vector layer to have a single grid cell if any of the input layers have a grid cell at that location. However, I don’t want the output layer to have "stacked" cells, so I don’t think merge, with subsequent field math, works.

How can I do this?