Yes, you can connect as many private nodes as you want within a overall limit of 32 I believe it is.
To get past that, I think you would need to edit the source code and recompile.
It would be suggested to use a obscure node number. Like 1120 or something like that.
The default pick most use of 1999 will cause you problems making a connection to others who also have a node 1999 connected. It’s a built in loop block protection that should never have been enabled inside of the private node area. But there it is.
Although you also have the possibility to add the extra digit to a node number and just not register it and it would be private and unique. That is the ultimate fix for that issue.