Don't go there. Most rods are already crazy-broken as it is. Metamagic without adding spell levels? Puh-lease!!!
You could have a greater, normal, and lesser version.
The price for stacking multiple effects is usually the price of the most expensive plus 1.5 times the price of all the other effects.
Because you are paying for the rods separately you should take their price out.
The average meta magic feat adds two spell levels so I would base the price off of those.
A minor +2 spell level meta magic rod is 9,000 if you were to combine 3 rods the total cost would be 36,000. (9,000 + 9,000*1.5 + 9,000*1.5)
Subtract the cost of each rod separately and you get 9,000.
The utility of being able to swap out the rods in the staff should be worth a little but not too much. I would say a decent price for a lesser version of this staff would be 10,000. The lesser version could only hold minor meta magic rods.
Following the same pricing a normal version would be worth 32,500 + a swap out fee so say about 35,000.
The greater version (able to hold major rods) would be worth 73,000 + a swap out fee, say 80,000.
how much would you price such an item, and how much additional would you charge for extra rod slots?
One first-born per rod.
I would probably price this at 2000.
I wouldn't go to overboard with the price because the same basic thing can be accomplished by duck-taping 3 rods end to end...
I came up with a similar but more versatile item:
Staff of holding
This staff can be given weapon enhancements like a normal staff in addition to having the below abilities.
This staff has 4 large grooves running along its length. Each groove can hold 1 magical staff, or 2 wands or metamagic rods, which shrink down and snap into place. The wielder can cast any spell from any of the slotted items or use any metamagic rod when casting a prepared spell as if they were wielding it.
As a move action, the wielder can make the entire staff function as if it was one of the staves slotted into it, but doing so negates any weapon enhancements that the Staff of Holding has and makes the other staves, wands or rods temporarily unusable. This ability can be ended as a swift action.
Non-metamagic rods can also be put into the staff, but only their spell-like abilities can be used, such as a Rod of Wonder. Rods with static abilities, such as a Rod of Absorption, can also be placed into the staff, but the rest of the staffs powers have to be suppressed with a move action as above for the rod to function.
CONSTRUCTION REQUIREMENTS
Cost, 2,500 gp; Feats, Craft Staff; Spells, secret chest
I think people are misunderstanding what he wants.
He just wants to save himself having to juggle multiple rods in hand by basically sticking them all together in one rod/staff. But he would still only be able to use one rod effect on each spell and would still have to buy all metamagic rods separately. He's basic trying to save himself some action economy of taking out and putting away rods.
It's actually a fairly reasonably request. I don't know how I'd price it exactly since it is a pretty potent effect.
A handy haversack would allow him to retrieve any stored rod as a move action and cost 1000 gp.
Putting a rod away so it's can be easily stolen or doesn't have to be dropped on the ground has never really been priced.
He could always tie multiple rods to his belt and pull them out to use them, and again putting them away safely becomes a hang-up.
I'm going to say something like this should cost somewhere between 5,000 to 10,000 gp. It's useful, but not amazing.