At the moment, the Influence needed to merge Cities together can very easily reach prohibitively high costs. It isn't uncommon to see the Influence needed to reach the tens of thousands, which is oftentimes far too much Influence than can be afforded. While this cost can be reduced in some ways (making sure that both cities have identical sets of Infrastructure can reduce the cost), it will still be rather expensive, and merging Cities will usually cost too much Influence for a fairly low return.

However, there is a far cheaper solution to the high costs of merging Cities - simply burn one of the Cities to the ground! Take a military Unit and start ransacking a City. Once the City is destroyed, you can create an Outpost in the same spot as the ruins of the City. Because the Outpost is created on top of Ruins, it will be established immediately. Afterward, you can simply attach the Outpost to your City, which will have a lower cost than merging a City. 

This strategy needs far less Influence, turning a cost of tens of thousands to only a few thousand at most. The only downside that it comes with is the fact that it takes a lot of time, needs a military Unit, and it also kills off all of the Population and deletes the Infrastructure of the City that's getting destroyed. So if you're merging Cities because you want to get a single high population one, then this strategy is considerably less useful. However, if the only thing you care about are the Districts, then razing a City will still keep the Districts in its Territory, making this strategy rather helpful for reducing your Influence costs. 

The fact that the Population will die when the City is ransacked can be mitigated somewhat by having the razed City quickly produce several military Units beforehand, or use Forced Labor to get a few Districts out - since the Population is all going to die anyway, they might as well die for a good cause. If you want to, you can have the City produce the very military Unit that's going to burn it down, which admittedly may be a bit messed up.

A similar strategy to this - ransacking Cities on purpose - can also be used to very effectively convert your Influence into Industry. When you acquire an additional Territory, you can choose to immediately turn it into a City first, using one of the Colony Plan-type projects. Upon doing this, the new City will instantly get a free burst of Industry and Population. 

Using this free Industry that it just got, the new City can immediately go and build several Districts. Because this one-Territory City does not have any Districts, all of these will be extremely cheap to build. You can also use some of the Population to rush out more Districts. 

After you're satisfied with the Districts that the City built, you can go and ransack it. Similar to the above strategy, you then turn it into an Outpost and attach the Territory, which will now come with a few Districts in tow!

This has an extremely low cost in Influence - creating the extra City and Outpost will cost a few hundred at most. In return, you can get several Districts. If those Districts were to be built in a developed City (such as the City that you're planning on attaching the Territory to), it would likely have cost thousands of Industry. 

If you wish to do so, you don't need to stop with one City. Upon creating the Outpost the second time, you can turn it into a City again, and get another burst of Industry and Population. The second City created will have diminished returns, because the District cost has increased, but the Influence can still be converted into Industry.