Is there a way to download additional guitar effects for the MBR?
Effects? No. Effects patches? Yes.
The BRs come with certain effects (chorus, flanger, delay, etc). There's no way to add more effects internally but you can create many combinations of the existing internal effects and settings and save them as User or Song patches. It's very easy to do. In principal, it's no different than if you had a pedal board with several stomp boxes on it. You can switch individual effects on or off by stomping on the switch and you can adjust any of the knobs and switches on the pedals. The great thing about the BRs is that, once you've made all of those "pedal" settings, you can save them as a patch which you can pull up at any time in the future.
As for downloading, there aren't a lot of patches available because very few people have uploaded any. But here are a few to try:
https://songcrafters.org/community/index.php?topic=9580.msg128122#msg128122 (https://songcrafters.org/forum/index.php?topic=9580.msg128122#msg128122)
https://songcrafters.org/community/index.php?topic=115.msg579#msg579 (https://songcrafters.org/forum/index.php?topic=115.msg579#msg579)
https://songcrafters.org/community/index.php?topic=96.msg410#msg410 (https://songcrafters.org/forum/index.php?topic=96.msg410#msg410)
Just enter the settings shown in those messages and save it as a User or Song patch. What's the difference? Well, a Song patch is stored on the memory card. This means you can have an unlimited number of Song patches. However, they can only be used in the song in which they were saved. You can't create a patch in one song, then later use it in another song. User patches, on the other hand, are stored in the BR's internal flash memory (not on the card). This means that they can be used in any song. However, there's only room for 120 User patches in the Micro BR. That's quite a lot but it's not unlimited like the Song patches. I usually find that I create a patch for a specific song then never have need of it again, so I save it as a Song patch. But if I ever come up with a really cool patch that I think I might use again in the future, I'll save it as a User patch.
Ditto what 64 G said! And the patches I usually save as USER patches are vocal patches! The only way to get new EFFECTS is by a firmware update, and that doesn't seem very likely just now !