You have a situation similar to mine, although we have less income and only one 401k to contribute to. Your MAGI needs to be less than $96,000 to contribute to a 401k and a traditional IRA. Napkin math tells me your MAGI is ~$120,000 - $35,000 = $85,000, give or take for other adjustments.
So, yes, you can contribute to Traditional IRA's and take another chunk off your tax bill.