Growing up, ‘multimeter’ was pronounced ‘mul-TIM-it-er’. Nowadays it seems I only hear it pronounced ‘MUL-tee-mee-ter’.
Dictionary-dot-com has the former pronunciation, and Youtube has the latter one. Granted, the Youtube pronouncer is English; but that’s what I hear in the Pacific Northwest and on the occasional TV show.
So which is the preferred pronunciation?
(FWIW, I say ‘al-TIM-it-er’, and I hear English people say ‘AL-tee-mee-ter’.)
It’s a multiple function meter or multi - meter…
I call it mul - tee - meeter with a bit of emphasis on “mul”.
Mult-ih-MEE-ter or Mult-uh-MEE-ter is what I always used and heard.
FWIW, I have never in my life heard of anyone anywhere saying Mul-TIM-eh-ter or similar. Though I’ve only ever heard Americans say it; that might be 100% standard Brit-speak for all I know.
Lab meters (e.g. Keithley 2001) are usually referred to as digital multimeters (DMMs). Handheld meters (e.g. Fluke 87) are usually referred to as digital voltmeters (DVMs).
Multimeter is pronounced MUL-te-meter.
Its a meter, not a tim, so it seems to me the emphasis on METER, not TIM is the way to go from a purely logical POV.
Mul-TIM-it-er, from extensive interaction with the ham, kit, board-level computer and hobby communities over 35+ years. I can’t remember hearing “MUL-ti-meter” or any other variant.
I haven’t heard any such differentiation for a long time, not since the handheld units went past volt (and resistance) measurements only. It may be an industry variant, or maybe certain engineering-ed tracks, that use the different terms.
DMM was never common in my worlds. DVM, a little but it always referred to multi-function units… mulTIMeters.
I was so proud of my Fluke when I bought it, at almost a month’s salary… and the one I just got free from HFT is still here on my desk. 
I grew up in San Diego.
Do you say ‘altee-meter’? 
This is the way I’ve always heard it (I’ve spent most of my life in the West Virginia, Pennsylvania, Maryland area).
I’ve never heard anyone pronounce it in a way that rhymes with altimeter.
Logically it ought to be Al-tih-MEEt-er. As billfish678points out. But for whatever fouled-up reason aviation settled on Al-TIM-ih-ter, so that’s how I say it. I always blamed the Brits for that one too; they seem especially good at putting syllable breaks in odd places.
Don’t get me started of the idiots behind kih-LOM-ih-ter or the habit some folks have of using the word “kilo”, a quantity multiplier, to mean a unit of mass.
I’ve never heard a Brit say ‘al-TIM-it-er’. I’ve only heard them say ‘AL-tee-mee-ter’.
It’s been many years since I took German in high school and college, but I still pronounce it ‘kill-oh-mee-ter’. (And I have to check myself so I don’t say ‘KEE-loh-may-tah’ (German pronunciation approximated.))
The Dictionary.com cite is the first time I’ve ever heard that pronunciation. I’d say multi-meter. And kill-OHM-mee-tah.
likewise. It’s a meter.
As is an odometer, which is generally called an oh-DOM-it-er where I’ve been in the US.
But I say Mul-tee-mee-ter. Always have.
that disagrees with me, so it doesn’t count 
MUL-TEE-PASS.
But what the heck is this odo we’re measuring? If you have two of them, are they odos, or odiea, or ???
It’s funny how you can use a word your whole life and never stop to consider how odd it is.
Isn’t that how the British say it? IOW, your “bias” is British for one word (multimeter), and, arbitrarily, it would seem, American for the other. :)
I think there actually is a systematic reason. To get to the OP: multi- is used–in American speech–as a combining form. Effectively, for Americans, it is more “lexematic.” So it maintains syllable stress, regardless of how it combines, and meter, as a result, maintains its syllable stress.
While kilo- is also a combining form, the OED speculates that words like speedometer (note that speed is a single-syllable lexeme, calling for a different combining form, -ometer, specifically used for that purpose, e.g., thermometer, etc.), have influenced the pronunciation of words like kilometer, which get pronounced either way in the States. My suspicion is that it has to do with “communities of practice,” a term which we use in applied linguistic to mean basically, “who you hang around with,” and how that influences your language.
Why this doesn’t happen in British English, I’m not sure, but it’s a fairly common thing.
Pssst… Check the OP. 
So I pronounce multimeter and altimeter the same way, not different ways.
Right, so why not be British all the way?
If you are a red head with a hot body, firm tits, and wearing a body thong you can pronounce it however you like