Multiverse of monsters

If I get "Multiverse of Monsters" does that add any new playable species to my character builder?

Yes it adds:

Aaracokra
Aasimar
Bugbear
Centaur
Changeling
Deep Gnome
Duergar
Eladrin
Fairy
Firbolg
Genasi (Air, Earth, Fire, Water versions)
Githyanki
Githzerai
Goblin
Goliath
Harengon
Hobgoblin
Kenku
Kobold
Lizardfolk
Minotaur
Orb
Satyr
Sea Elf
Shadar-Kai
Shifter
Tabaxi
Tortle
Triton
Yuan-ti

If you mean Mordenkainen Presents: Monsters of the Multiverse, then the answer is yes. That book includes 33 playable species options, and if you purchase the digital version on D&D Beyond, you'll be able to use them in the character builder. 

Note that this book was written for 5e, and while the species options in it should all work fine in 5.5e rules, a few of them (Aasimar, Changeling, Goliath, Orc) do already have 5.5e updated versions that supersede the ones from Monsters of the Multiverse.

I see that the compendium was written for 5e, is it possible that the species just for 5.5e don't show up when you are creating a 5.5e character?

Thanks for the answer and anything additional you might add.

All races/species will show available for character creation, as long as the relevant toggles are enabled on the Home tab of the builder.

2014 Core rules will enable PHB 5e species
2014 Expanded Content will enable all 5e species from all official books beyond the core books that were not reprinted into 5.5e
2014 Legacy will enable all 5e species that were reprinted into 5.5e to still be selectable, if you prefer those versions or don't have access to the 5.5e book.

So ensure all 3 all enabled and everything from Monsters of the Multiverse will be selectable.

Quote from Cyb3rM1nd >>

All races/species will show available for character creation, as long as the relevant toggles are enabled on the Home tab of the builder.

2014 Core rules will enable PHB 5e species
2014 Expanded Content will enable all 5e species from all official books beyond the core books that were not reprinted into 5.5e
2014 Legacy will enable all 5e species that were reprinted into 5.5e to still be selectable, if you prefer those versions or don't have access to the 5.5e book.

So ensure all 3 all enabled and everything from Monsters of the Multiverse will be selectable.

For the record, the options are actually called "5e Core Rules" and "5e Expanded Rules". The "Legacy/Noncore" option is for sources like Volo's Guide to Monsters that are out of print and considered fully superseded within 5e itself; you don't need to enable this to see 5e species that have been superseded by 5.5e options.

The only option you need to enable to see all the options from Monsters of the Multiverse is "5e Expanded Rules".

Aye sorry. Was eating dinner when posting that and went off memory instead of checking first. Thank you for the correction.

Thanks!

Thanks!