The vast majority of march capacity is determined by your castle. This does not mean that you should not concentrate on anything else, but if you reach the maximum of level 40 at your castle, the marching capacity alone will be increased by 170,000.
The increase per Castle level starts at 2000 and increases every 5 levels by another 500 until it reaches 4500, which you get for level 26-35. After that it makes a jump. For the last 5 levels, you will receive 10,000 each.
At castle level 31, you also get a march capacity increase of 10%, which does not increase further for higher levels.
War contains 4 researches that offer an increase in marching capacity of 10,000 each. War II contains two researches, which also offers a capacity increase of 10,000 each, so the research can provide you with the nice extra capacity of an extra 60,000.
Lord Talent Points
Lord Talent Points in WAR section can increase your march capacity with 15,000, split into 3 projects of 5,000 each. In addition, the War Tree contains the Colossal Marts talent with a 10% capacity increase (for 30 minutes).
You can increase the number of troops in the airship with the March of fury ability. In conjunction with the Intensity Gears, you can send up to 64,000 more troops here.
Total Intensity Boost x total bonus 'March of fury' = total marching capacity bonus
Guardians have three options to increase their marching capacity.
Madame Lannoy brings a boost of 23,000 at 4 stars.
Jules Marazin even gives you 25,000 more capacity for 4 stars.
And in combination with the dashing duelists (for example, D'Artagnan), there is already 25,000 more capacity for one star on your marches.
The commander's horn gives an increase in capacity by 15%. You can buy it for 2000 gold. The boost is active for 1 day.
There is one item in the Gold Shop that will increase your marching capacity by 25% for 12 hours for 1500 Gold. There is a similar item that offers the same boost for just 2 hours. I do not think you can buy it in any store, but it's a potential event rewards.
In the Auction House, it is possible to offer items on 3 12h colossal march capacity that offer a 50% increase for 12 hours. I have seen bids for these items from 25,000 to 60,000 gold.
With the title 'standard bearer' there is in addition to the already existing capacity of 5%. The title can be given by the king to any player in the kingdom.
It's possible to get up to 502.950 troops to send in a march!