Jack wrote:

1000 sq ft basement getting finished. I would like a combination
dehumidifier, heater, air exchanger unit. (No A/C). Is there such a thing?

Maybe.

I need a dehumidifier in the summer,

Sounds like you have air leaks or a slab with no vapor barrier.
You might run an $80 window AC when the indoor RH rises to 60%, using
Honeywell's H46C1166 humidistat, $60 as Grainger's stock no. 2E574.

heat in the winter (sometimes), and always-on air-to-air exchanger.

Most houses naturally leak ten times more fresh air than required,
making air-air heat exchangers expensive and useless. In mild weather,
you might run an exhaust fan if the indoor RH rises to 60%.

For heat, you might run a window AC inside the basement in wintertime,
with a solenoid valve and a soaker hose that dampens the slab if
the basement RH drops to 50%, using an Autoflo 052000 humidistat,
$31 as Grainger's stock no. 2E453.

Nick