DXF format does not really support multipoint geometry type and therefore GDAL DXF driver https://gdal.org/drivers/vector/dxf.html can't handle them. FME does support multipoints with a workaround by storing them as blocks
https://docs.safe.com/fme/2018.1/html/FME_Desktop_Documentation/FME_ReadersWriters/acad/Geometry-Support-acad.htm
What you can do with ogr2ogr is to explode multipoints into simple points https://gdal.org/programs/ogr2ogr.html
-explodecollections
Produce one feature for each geometry in any kind of geometry
collection in the source file
Proof of concept:
ogr2ogr -f dxf multi.dxf multipoint.jml
ERROR 1: No known way to write feature with geometry 'Multi Point'.
ERROR 1: Unable to write feature 0 from layer multipoint.
ERROR 1: Terminating translation prematurely after failed translation of layer multipoint (use -skipfailures to skip errors)
ogr2ogr -f dxf multi.dxf multipoint.jml -explodecollections
Conversion succeeds, now check the result:
ogrinfo multi.dxf entities
INFO: Open of `multi.dxf'
using driver `DXF' successful.
Layer name: entities
Geometry: Unknown (any)
Feature Count: 3
Extent: (500.000000, 360.000000) - (590.000000, 454.000000)
Layer SRS WKT:
(unknown)
Layer: String (0.0)
PaperSpace: Integer(Boolean) (0.0)
SubClasses: String (0.0)
Linetype: String (0.0)
EntityHandle: String (0.0)
Text: String (0.0)
OGRFeature(entities):0
Layer (String) = 0
SubClasses (String) = AcDbEntity:AcDbPoint
EntityHandle (String) = 20000
Style = PEN(c:#000000)
POINT Z (590 454 1)
OGRFeature(entities):1
Layer (String) = 0
SubClasses (String) = AcDbEntity:AcDbPoint
EntityHandle (String) = 20001
Style = PEN(c:#000000)
POINT Z (513 411 2)
OGRFeature(entities):2
Layer (String) = 0
SubClasses (String) = AcDbEntity:AcDbPoint
EntityHandle (String) = 20002
Style = PEN(c:#000000)
POINT Z (500 360 3)