Yes, they can. But even easier is transplanting the runners which appear around the base of the plant. If you buy one of each of the varieties you want you can increase your stock thereafter. But I would recommend buying the beginner plants from a reputable dealer who guarantees the variety and the virus free status of the stock. Hand me down raspberries can bring disease into your garden.

If you are talking about black raspberries you can increase them by layering.

Thx for your suggestion--I will follow it. Sorry I took so long to thank you.

I have a large number of runners from my everbearing raspberry. When do you dig them up/cut them free from the mother for transplant?

Charlie,

Here in the PNW I dig anytime it's not really hot and dry or freezing cold. What you want is the crown and some roots to survive. Once the start is dug, I cut back some of the top, leaving enough leaf to feed the root until a new shoot starts going up. If you have not enough root and the top leaves start to wilt, just chop off a little more leaf /shoot.

Raspberries here are in the category of, " It -seemed like a good idea at the time". So be careful what you wish for, someday you may end up like me, knowing no matter how many I dig and give away and put in the recycle bin, there will still be raspberries increasing in the back garden after I die. Every time I think I really have ALL of them out of an area, new babies poke up later as a surprise. Yelling at them doesn't seem to help either.

I just pulled up a hundred or so this morning without much trouble...the soil is very wet this week.
I'm in a very natural wooded landscape as are the neighbors. We call it 'easy care', lol.
I do have an area out front and up the hill where i let them go a bit free. About a ten x 20 area and just prune, snip, and pull this time every year. Takes an hour a couple times.
I pick a couple qrts every evening through the summer and freeze the overflow.

They do pop up everywhere, where i don't want them, but the return is amazing fresh berries.
(i do warn those that want them of the spreading, mostly by birds me thinks)