Yes you can.
You are not obligated to stick with an attorney just because you initially hired him or her. If you are dissatisfied with their work, you have every right to leave and take your case to another lawyer.
However, be aware of this fact:
The attorney will have a 'lien' against all work that he has done up until that point. That means that if you are ultimately successful in your accident case, negligence case, medical malpractice case or wrongful death matter, the two lawyers- your first lawyer and your second lawyer will then have to battle it out and determine how much of the attorney's fee they are going to split.
You will not be involved in that fight. Many times the attorneys can work it out on their own to determine the fee split between themselves. Remember, there is only one legal fee. Your first lawyer is entitled to a percentage of that fee. The only question becomes 'how much'.
If the lawyers cannot agree on their respective fee split, they will take their fight to the trial judge who supervised your case. In extreme cases that can result in hearings and sworn testimony.
In any event, you have an absolute right to take your case to any attorney you choose at any time you want. Keep in mind that there are some lawyers, like myself, who refuse to take on a case that was started by another attorney. However, the answer to the question is "Yes, you can do that."
To learn more about this topic, I invite you to watch the quick video below...