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You can map as many fields as your would like, however, I believe the selection of objects is limited. However, I haven't tested it, but it should be possible to integrate with custom object of salesforce by taking advantage of our Zapier. Please check the following guide: http://www.jotform.com/blog/65-JotForm-is-now-on-Zapier-Send-Your-Form-Data-to-100-Web-Services
Basically you will have to create your own Zap to create custom object when new submission is received. Please check the screenshot below:
Other than that, I believe our integration is limited to the objects in the menu.