What you are looking for is to have the power in the 400-um fiber to have close to its equilibrium distribution among the available modes by the time it exits the fiber.
Without special care, the launch from the 9-um fiber to the 400-um fiber will excite only a (probably fairly small) subset of the available modes. And 1-5 m of fiber is likely not enough on its own to allow the optical power to redistribute itself among the modes.
I can think of a few ways to get closer to an equilibrium distribution at the fiber exit:
At the single-mode to multi-mode transition, try to increase the number of modes excited by defocussing the beam so as to get closer to an equilibrium mode distribution on launch. This will likely degrade the coupling efficiency resulting in less power being launched into the multimode fiber.
Put some fairly tight bends in the multimode fiber so as to encourage redistribution of the modal energy. This will cause power loss as some power is coupled into cladding modes or even radiating modes.
Increase the length of the multimode fiber to allow the power to naturally redistribute between the modes due to imperfections in the fiber along its length.
Unfortunately I don't work with 400-um fiber so can't give more specific guidance on how to re-focus the launch beam, how tight a bend is needed to redistribute the modes, how long a fiber is needed to redistribute the modes, etc., but you should be able to work these things out with some fairly simple experiments.
Also, as I've mentioned, all these methods are going to increase optical loss, which could be a problem depending on your overall requirements.