many will if they produce flowers from the lower leaf joints [axils]. some are terminal flowers others axil. it was one of the features of Mendels work on genetics.

Wow. Fascinating. I'd never heard of Mendel's Laws. I'm off to read some more . . . . . thank you.

Save your eyesight. God knows how Mendel got into advice on sweet peas :)
but,

Every leaf joint on a sweet pea will produce a flower stem.
At the same time, every leaf joint will produce a new lateral stem which will then grow and eventually produce a flower from each of it's leaf joints. And so on and so on ad- infinutum.
Unfortunately, the length of the sweet pea stem rapidly diminishes if you grow like this, so unless you buy a vase the size of an egg cup, they won't be much use.

So yes, in theory you can.

This would be perfect for what I want in one particular place. I'll have a go, and post a pic later in summer when there is a result. I'll still keep the full height on the main cutting crop over the fence.
Now, . . . on to tackle the greenfly. Shame there is a real lack of ladybirds in Argyll.

Mendel was an austrian monk with the responsibility for the monastry garden and feeding all the others. So as a keen mathematician he started counting pea shapes and colours and wether they were smooth seeded or wrinkled. To cut a long story short he noticed patterns and a mathematical theory was born. And all before the discovery of chromosomes and DNA :o)