"I suppose I could stay more time"

"I suppose I could stay more time"
 

"I suppose I could stay more time."
if someone says this it means they were planning to leave earlier, but are thinking about extending it or at least entertaining the possibility. What would the translation to Spanish be? I'm not sure the literal translation makes sense:

"Supongo que yo podría quedar mas tiempo"

It makes sense. Use más and not mas.

hmmm. I used the phrase on my wife and she didnt' know what the heck I was talking about.

I believe she'll understand if the pronominal form-quedarse-is used. ;)

Still not. She's saying it's an odd use of "suponer", that she wouldn't say it like that. I asked her to give examples of how she uses the verb and her examples seem to be equivalent to "expect" or "anticipate"... so i guess that's where the confusion lies.

Suponer in various forms has more meanings than its English counterpart, but it certainly means to suppose.

If you are not comfortable with suponer consider using imaginarse. It is used a lot.

or revert to basic language and just say "tal vez yo podria quedarme mas tiempo."

You may say "Creo que podría quedarme más tiempo".
This gives the idea of reckoning or considering. Maybe that's what she's expecting.

Poli's suggestion to use "imaginarse" is fine too for me. :-)

O supongo que podría quedarme algo más de tiempo/ unos días más.

I agree with the prior translation, though I would add another option "Podria extender mi estadia" when the family is visiting and want to stay longer than planned. Hope it helps.