So i guess you had an answer to your question before posting. Nothing will stop you from multiple application, but you need to be aware of the guidelines and the involvement of the three offices. Apart from PR application and dual intent, you can have 2 application at the same time if one is in litigation. this brings question of ceremony and retirement for successfully and un successfully application respectively. Not advised simply because you have two work offers, all other details will be the same and system will pick during cross matching process, eventually delays your application...