OP, to actually answer your question. Someone above hit on it. You can't 1031 into partnership shares, so the only way to do it is something called Tenant in Common (TIC). TIC deals were all the rage in the early 2000's but they have fallen out of favor because they are disasters to manage. Everyone owns a direct piece of the property, which means everybody has to agree on everything to manage it. Imagine if one guy doesnt want to sell, when everyone else does, it becomes a pain. On top of that, the biggest problem are capital calls. Most TIC buyers were like you, they wanted to leverage into something bigger with less headache, but they didnt have excess funds laying around. So, when something went wrong, people had to pay up to cover the problems, and lots didnt have the money. Plus, you are suddenly tied to the whims of a group, and with 1031, you have to be ready to move it again to keep up with it. Bottom line, stay away from these.
1031 as a strategy is "Swap til you drop". Once you are on the wheel, you cant get off. Then, when you die, your heirs get a stepped up basis and the taxable gain goes away. I wouldn't be surprised if this goes away in the next tax bill.
The new tax bill did introduce an unprecedented concept having to do with qualified investment zones. Basically, if you are in certain areas, after 10 years, the gain goes away. I'm only starting to hear about this, and people are just now figuring it out. So, I dont know much beyond this.
I think 1031 is overused. Its a pain in the ass to deal with, and for the amount of money you are talking about, it might make sense to just pay your taxes and move on.
Im not an attorney, or a tax professional, or anyone else you should listen to.