<p>^ If you absolutely think doing both is beneficial.
Nobody will stop you if you find both interesting. I just don’t think it’s good to major in BME and Mechanical as undergraduate. However, I find it makes sense to major in Mechanical and computer engineering for my friend who is interested in robotics and AI (and she’s in robotics team).</p>
<p>Graduate school? There are companies that are willing to put you on non-thesis graduate program 
If you are not sure graduate school, then get a job afterward. Most people choose to get a job to afford their graduate studies.
This is also a reason why it’s better to major in a different engineering if you are not sure about BME’s opportunity in the first place.</p>