Layover en route to Tel Aviv

On the airline site just choose (multi city) instead of one way or round trip. Sometimes this is hidden under "Advanced".

Knowing your origin point would be helpful if you want specific suggestions

We originate in Shreveport, LA (SHV). The basically two airlines out of here connect in Madrid (where we've never been) or Frankfurt, where we have been.
We originally planned to go to Greece for a few days before meeting our tour in Tel Aviv (TLV) but doing a multi-city itinerary was much more expensive. We haven't ruled out RT to TLV with another RT to Athens for 4-5 days after arrival in TLV and before the tour in Israel-much less expensive-anyone see any problems with that?
hope that's not too confusing

Turkish Air flies out of Houston. You could spend a few days in Istanbul. My last 3 trips to the US have been on Turkish and I find it more comfortable and with better service and better entertainment than most other airlines. From Istanbul to Tel Aviv is a 2-hour flight and same time zone, with multiple flights a day, so you could easily get from IST to your tour group on the day the tour begins.

Both El Al and Aegean have frequent flights from here to Athens, again 2-hour flight and same time zone. In March the R/T price is less than $250.

I’m from Shreveport too! CSHS, go Gators.

From the Port, you can easily get to DFW, ATL, CLT and Houston. From there, you can go anywhere. As others have said, use the multicity function on Kayak.com. Absolutely no need to waste money on a travel agent. Enjoy Israel. I go every year.

Another option to consider, if a layover on the way back is possible, is to book round-trip to your city of choice for the layover, then book round-trip from that or another city to Israel. Sometimes a long layover can come at a premium price, and you may be able to find a more budget option to Israel from Europe.

Consider Cairo, visit the Pyramids and the Egyptian Museum.

Several years ago, I went on a small group tour of Turkey (out of New Orleans) and was struggling to find a cheapish fare roundtrip to Istanbul. Turkish Air was the obvious choice.... but still was charging more than I wanted to pay. Then, somehow, I discovered that if I booked through Turkish Air roundtrip to Tel Aviv (through Istanbul) I could book it with a LAYOVER of 10 DAYS in Istanbul on the way back and my fare went down by approx. $400. I can only guess that Turkish Air was trying to fill seats on its IST-TLV legs. So... I spent 6 days in Israel at the top of my trip to Turkey! I wonder if Turkish Air is still offering similar lower fares to TLV through Istanbul? Worth checking out. And Istanbul is a magnificent city worth however many days you can schedule there!