No one can be legally married twice, so the ultimate answer to your question is no.  
 
If you are civilly married you cannot be married in the temple marriage is a civil marriage. You can be sealed to your legal spouse in the temple though, if want to have a civil union and later be sealed.  
 
This will be the case for my wife and I because we were married when she was a non member and I was inactive so we couldn't have a temple marriage. Now that she is a member we are preparing to be sealed in the temple.  
 
The Church doesn't recommend an LDS couple to have a civil marriage and to later be sealed, unless there is a situation that makes getting a temple marriage unreasonable.  
 
I know that before there was a temple in Raleigh NC, many couples would be married civilly and later attend the Washington D.C. temple to be sealed.  
 
This is the same for many couple in places where the Church is still developing, there is places where going to the temple requires a lot of time and money to accomplished and in those situations it is recommended that couples civilly marry than later be sealed.  
 
Now ultimately it is the couples decision to make there is no rules that I know of that say you cannot be civilly married and then later sealed if you are an active LDS couple.  
 
I know that lots of times when an LDS couple is sealed in a temple that there non member friends and family (and member friends and family that don't hold a current temple recommended) will go to the temple with them and wait outside and view the temple grounds while the ordinance if performed. Then all will go to the reception and celebrate the couples union together. Larger temples even have missionaries available to explain how the sealing ordinance works and every temple has beautify grounds to tour.  
 
I know it isn't the best situation and that some family and friends may feel offended that they cannot enter the temple, but the temple is holy ground and not everyone is allowed inside the temple.

What happens to a couple if they divorce? Can the woman be sealed to her next husband without seeking anyone's permission, same goes for the man. What if you're married 2 or 3 times. Who gets to call you over to the other side?