"There is / there are" with participles

[DinghyDog]

Hi Everybody,

Everybody knows the simple "There is / there are" construct:
- There are six radiators in this house.

Can this construct be adjusted. How much?
- There exist six radiators in this house.
- There should be six radiators in this house.
- There should exist six radiators in this house.

With participles?
- There are six radiators installed in this house.
- There should be at least six radiators installed in this house.
- There are six people sitting at the table.

Most of the examples (especially the ones with past participles) sound awkward to me so I tend to correct them while verifying other people's texts (technical, with lot of passive voice), e.g.:
- At least six radiators should be installed in this house.

Please advise,
Adam.

[Alan]

Yes, your examples are all possible.