I would recommend not doing what you suggest, here's why:
A typical rough-in for a clothes washing machine is as show in the picture below and consists of the following:
- vent
- 2" p-trap
- vertical section of 2" pipe above the p-trap
- (an actual outlet box as shown is not required, you can just use the plan end of the pipe)
Your discharge hose will fit inside the 2" pipe opening and will usually enter the pipe about 6" to 8". This connection is not water/air tight.
The size of the p-trap and the vertical section of pipe are to accommodate for the flow rate of the washing machine's discharge. The p-trap will create a restriction to the flow and the vertical pipe allows for some head water to buildup without putting any back pressure on the washing machine's internal pump.
A p-trap is a must as it will prevent sewer gas from entering your house. The vent is required to protect the water seal of the p-trap but can be replaced with an air admittance valve depending on local codes.
I would imagine that if your machine can pump that high it will be near its limit and without any room for a vertical section of pipe to discharge into you will have to make the connection sold which will put additional back pressure on to the machine's pump (even more due to the pipe size only being 1.5") which will shorten the life span of the pump.
In homes where there are no drain lines in the basement floor, it's common practice to use some form of cistern containing a pump. A quick search at Home Depot turned up the SANISWIFT®, made by a company called Saniflo. The specifications list this unit as having a vertical discharge of 14 ft., which should be more than enough.
I've seen similar setups in many basements, where the only drain available is overhead.
Grey water from the sink and washer are collected in the cistern, then pumped up and out of the area when the cistern is filled to a certain level.
If the washer discharges faster than the grey water pump can handle, you're going to have problems. That's why when installing a system like this, the cistern should always be large enough to hold more than the volume of water that will be discharged by the washer. In the above image, the sink acts as a secondary reservoir (as well as an air gap) allowing the pump extra time to discharge the water. If you're not using a sink it's a good idea to have a larger cistern, and/or a grey water pump that can handle the volume.
You'll also want to install a check valve, on the discharge line from the grey water pipe. This will prevent the water in the vertical pipe from draining back into the cistern, and causing a potential infinite loop situation.
As for whether or not you should rely on your washing machine discharge pump to lift the water, you might find this related question useful.
WARNING:
This is only appropriate for grey water discharge. This method is NOT appropriate for sewage discharge.
Obviously there are other manufacturers of other systems, and you could always build you own system. I do not recommend or endorse this product, it is only used as an example. Searching for grey water pump
will find many alternative products.
Best Answer
You're correct, the requirement for washing machine drain is 2".
To determine if you have enough drain capacity for an additional machine, you need to consult the Uniform Plumbing Code's Drainage Fixture Unit values and ensure the total fixtures don't exceed the capacity of the drain for your laundry room (or plan an upgrade.)
These tables should help get you started: