This is a question which sticks in my mind because I like a blade work focused approach to epee. I also think the specificity of the question is good. Blade takes differ in each of the weapons, so considerations for a blade take in sabre or foil would be a little different than some of the considerations for a blade take in epee.
Many epeeists have also voiced frustration that as much as they practice blade takes it can be hard to effectively get the opponents blade, particularly in an offensive blade take.
So one element of the answer is to get the opponent to extend the blade.
Making feint-beats, or making feints toward a hit at the wrist might draw the opponent's hand upwards and more forward as they position themselves to be more ready for the action they believe you are setting up.
A partially extended blade closer to line with your target is easier to take than a partially absent blade. If taking the approach of drawing the opponent out you have to be ready either for their partial movement or for them to actually counter. It is a sad mistake to feint to draw a response and not be ready for the potential responses.
Mechanically speaking, be mindful of your hand wrist and arm position as these will set the position of your blade and define how your blade moves relative to your opponent's. The more consistent you make these elements the more control you will have and the less attention you will need to the details of the movement. Consistently practicing your blade takes with mindfulness of these elements will help you understand how the blades move and help you more naturally work with the leverage of the blades as they move together.
A mechanical element to consider is the positioning of your blade and bell relative to their blade. A blade take which locks their blade between your blade and bell, such that your weapon creates opposing contact points using your blade and bell will create more friction and more leverage making it harder to immediately disengage off from your blade take.
In practicing and drilling, once you have the basic blade take down and are able to lock the blade in the blade take and control the leverage have your drill partner simulate actual blade motion.
Epeeists frequently make small movements of the blade. These small rotations and small movements side to side make the blade harder to take. In part, the blade is not clearly in one place so the timing of the blade take is more difficult. Further the blade is already moving such to disengage as your contact begins, so a slower blade take may be less effective because they will slip off.
Have your drill partner move the blade simulating the types of movement and preparations you see your opponents making and drill taking the blade against that more realistic scenario.