As far as I'm aware, Exodus does not support multiple wallet files for one instance (unlike Electrum)... So, there is no way to specify a new wallet file location etc. Unless there is an undocumented "-datadir"-like commandline option that I'm not aware of.
However, I've found a slightly "hackish" way of doing it... basically... enable the developer options menu (ctrl+shift+d), then under "Exodus -> Developer -> Data Folder -> Open Data Folder" and find the location of your data folder... On Windows 10, this appears to be "%appdata%/roaming":
ie. "C:\Users\USERNAME\AppData\Roaming"
The folder locations for the specific OSes are listed here:
Mac: Hard Drive > Users > YOUR-USERNAME > Library > Application Support > Exodus
To get here, open finder, and press Command + Shift + G. Copy and Paste this into the Go To Folder text field: ~/Library/Application Support/
Windows: C: > Users > YOUR-USERNAME > AppData > Roaming > Exodus
( Windows users may need to show hidden files to access this folder. )
Linux: home > YOUR-USERNAME > .config > Exodus
You'll see an "exodus" folder... and inside that, a folder labelled "exodus.wallet". If you shutdown Exodus, and then rename that wallet folder (for instance: "exodus.wallet" -> "exodus.wallet.OLD") and then restart Exodus, it will generate a new "exodus.wallet" folder with new wallets/addresses etc.
Then, when you want to go back to the original wallet, shut down Exodus, rename "exodus.wallet" -> "exodus.wallet.NEW" and rename "exodus.wallet.OLD" -> "exodus.wallet"... and then restart Exodus... it will load up your original wallet with your original addresses.
NOTE: I have NOT tested this with any Exodus wallets holding coins... I accept no responsibility for any funds lost by messing with wallet folders! 
Other than this process, the only other things I could think of would be running Exodus under another user profile on your OS, or run it in a VM or something like that.
