Thank you for reaching out for help with your Monstera adansonii ("Swiss Cheese") plant.

While Monstera are not immune to pests, yellowing of leaves with brown brown spots is more commonly due to a watering problem.  Alas: it could be over-watering or under-watering...but the former is more common especially in the winter months when the plant's growth slows.  Brown spots can also be caused by sunburn;  but if you have kept your plant in this same location for the last two years and are only now seeing the brown spots, then the problem is probably not due to direct sunlight (unless something's changed outside your window...? Trees removed allowing more direct sunlight?).

Here are some things to check to determine if your plant might be suffering from overwatering:

1. On your diagnosis worksheet, you didn't answer the question about drainage holes in the pot.  I imagine you do have working drainage holes because you'd probably have drowned the plant sooner; but  this is essential, so check to be sure the pot drains well.
2. Have you reduced watering for the winter season?  Be sure to let the plant dry out thoroughly between waterings.  I put a finger down into the soil medium 1-2" to be sure there's no moisture there.
3. What soil medium are you using?  An aroid mix is ideal for Monstera.  You can make your own from meat moss, perlite and orchid bark, but it's easy enough to buy a good aroid mix ready-to-use and it will provide good drainage.
4. Can you measure or estimate the humidity?  Monstera are tropical vines that do best when the humidity level is above 60%.  (Right: they don't want wet roots since they grow largely in the air....but their native environment is tropical.)

Many of our Vermont homes lose humidity in the winter (with all of our heating...);  so it helps to mist leaves and, of course, the best course of action is to add a humidifier (or place the plant in a nice, warm bathroom that gets indirect sunlight and shower steam... :-).  But you can also use a pebble tray if adding a humidifier is too big an investment.

Since Monstera commonly require repotting every two years or so: if you have not repotted since obtaining the plant, now would be a good time to consider doing so. That would give you the opportunity to check the plants roots to be sure they aren't waterlogged and beginning to rot. (Oh dear!)  Even if you do not repot: taking the plant out of it's pot is the way to check the health of its roots.

If you review all of this and conclude that you have the opposite problem (underwatering can cause the same symptoms...):  then watering more frequently is the answer.  This is far less common ....but if you determine that you've been under-watering, you still don't want the plant to have soggy roots;  so be sure to provide good waterings and still allow the plant to dry out well before watering again.

Finally:  you can remove affected leaves -- but don't cut over more than 25% of the plant in one pruning.   You can propagate Monstera from cuttings and I would chose to do this if I discovered that my plant's roots were soggy/dying.  

Here’s how to propagate Monstera adansonii by stem cuttings:

1. Trim off a 6-inch stem piece, cutting just after a leaf node, so it stays intact
2. Remove any bottom leaves, a third to half of the cutting.
3. Apply a rooting hormone to the cut end.
4. Plant the cutting(s) in moistened soilless potting mixture in a small pot with drainage holes.
5. Place it in a warm area where it can receive bright light/indirect sunlight – avoid direct sunlight.
6. Keep the growing medium evenly and lightly moistened.
7. After a few months, you should have well-formed roots, after which you can transfer the cuttings into a larger pot.

Finally, here are two other possibilities (less likely, but I'd be remiss if I didn't mention them):

 1) Insects:   Do check closely to be sure your plant isn't infected with aphids, spider mites, whiteflies or scale (insects, i.e.);  I can't assess this (lesser) possibility from the photos.  

 2) Salt/Fertilizer Toxicity:  this is sometimes evident by a buildup of a crust on the surface of the soil or around the edge of the pot where the soil sits.  Here's a link to a University of Maryland Extension fact sheet on this:   
https://extension.umd.edu/resource/fertilizer-toxicity-or-high-soluble-salts-indoor-plants/

I hope you are able to help your Monstera!  I have a Spathiphyllum that has to remind me (well:  not every year...!) to slow down my watering and start misting it after we've turned on the heat for the winter.  I also stop fertilizing during this season since the plant's growth has slowed.  I hope this might just be a seasonal reminder from your Monstera.  :-)

Robilee Smith