Not a fan of courtship or dating. I prefer friends and then marriage without the intermediate steps (See Pride and Prejudice where the immediate response from a revealed attraction is a marriage proposal). That might have really confused a recent lady friend though, and I do not have a second wife, so you should probably ignore this. For children (not minors) at home I advocate arranged marriage.
I think there is nothing wrong morally with having more than one simultaneous prospect.
However, I think in practice it would be very stressful. One prospect at a time already seems very stressful. However, I am sure every family is different.
This seems ideal in Western culture.
In other areas of the world, i.e. many Asian countries, there is no concept of friendship between men and women without romance. I made 2 mistakes trying to be friends with women here:
1-I saw a girl crying after service and I approached her. I got her cell phone number to coach her (I was a regular speaker at that congregation at the time and she's in the flock). I texted her and encouraged her a few times with bible verses. She asked me if I could meet her for a coffee sometime; I declined. A year later I found out that a friend had been told by that girl's family members that she and I were "involved' and that it was "very serious"!!?!??!?!
Keep in mind, I never ever met her outside of the congregation and never even talked to her on the phone. I don't even remember that girl's name. Granted, she may be a special kind of crazy but follows is story number 2.
2-There was a nice grandma at the same congregation. Her husband works abroad and she sees him maybe a week every 4 years. Yeah, I'm certain dude has another family anyway...she's a physics professor and I studied a ton of physics so we became what I thought was friends. She attends the same congregation where I was teaching.
She is about 25 years older than me. She has no children and gave me a nice shirt one time. I thought the dynamic was a bit like a son figure to her so I accepted. Again ... wrong, she thought I was romantically interested.
What?!?! My wives explained to me that in this culture, men and women are not friends so that even a woman old enough to be my mother, who is married, thought that I was sending her romance signals when really I was just wanting to be friends with someone in need and with similar interests.
So ... the friends first advice works, assuming you are in a culture were there is not the constant looking forward to the post-friends phase which I think also happens to some degree in the states no?