Editing basemap in ArcMap

Bare with me here, because I believe I have a round about way of accomplishing what you want to do that involves ArcGIS Online and QGIS, because you can’t do what you want to do in ArcMap. I am going to make a couple assumptions here and if they’re not correct then I think you should take a different route then what I am about to write about. You don’t have access to ArcGIS Pro, otherwise all this would be much simpler task. You are willing to use QGIS, but for the most part you like the look of the ESRI basemaps and would like use their styling as much as possible except for a few tweaks here and there. You have access to ArcGIS Online. You have checked out the MapTiler QGIS plugin and maybe are not in love with their available basemaps. If all that is accurate then maybe try the instructions below.

There is a browser tool called Esri Vector Tile Style Editor that allows you to edit all elements of the vector base maps that Esri provides (or any that you have access to) including symbology, layers, scale level, etc. You will need to have an ArcGIS online account to access this tool. The instructions provided below show you how to change the ocean color to grey and bring it into QGIS, but there’s much more you can do it with it and I might recommend clicking on different elements to see what else you might want to change.

1. Click this link to access Esri Vector Tile Style Editor and sign in using your AGOL credentials.

2. Select the vector tile base map that you would like to edit. I have selected World Navigation Map for ease. The more complicated the symbology the more elements you will need to change.

3. Right off the bat, you’ll notice 4 map frames that show you what your edited vector base map will look like at different scale levels. At this point, it is best to set the different map frames at the scale level that you will be using for your own map. If you only really need one scale level, then I would focus on the main map frame, but the other map frames are helpful for if you will be using this base map for interactive map purposes.

4. The second icon on the left is the quick editor and allows you to make sweeping changes to the entire base map. If all you’re doing is trying to grey out features, then this a perfect way to quickly accomplish that. Click the symbol for water and change it to the color of your choosing.

5. The layers icon brings up an editor that will allow you to get more granular. In the picture below, you can see that it brings up the symbol and label options for the wide array of different kinds of land cover. This helpful for seeing what kinds of features are shown on the map; stuff that is easy to overlook.

6. However, by far and away my favorite way to edit is to simply click on any feature or label on the map. Doing so will bring up the editor for that particular element group/type. Try clicking on any label, land cover, or symbol. In the examples below I have decided that I don’t like the grey labels for my grey oceans and would like to turn them pink. By clicking on the label for the “North Pacific Ocean”, a panel will be brought up which allows me to edit the text, all ocean labels will now be pink. You can click on literally anything and edit the group/type it is a part of.

7. There are more editing tools available by clicking on the other icons on the left hand side, but lets assume that this base map is ready for use. Click the ‘Save’ Icon on the far left side. Name the base maps, choose the tags, and choose who the base map should be shared with. Once you hit save, the new edited base map will be in your AGOL content.

8. Navigate to ArcGIS Online and sign in using your credentials. Once you are logged in, click on the ‘Content’ button in the top center of the page. Maybe make sure that you are on the “My Content” page. You should see your recently saved tile layer at the very top; click this item to be taken to the item’s page with all the details, options, usage, settings, etc. Leave this page open for now. We’ll come back to it later.

9. Open QGIS. Right click on ‘Vector Tiles’ located in the browser panel and select “New ArcGIS Vector Tile Service Connection. If you do not see this option, you will need to update your QGIS to the latest version.

10. Go back to the ArcGIS online item page for the tile service. Scroll down to the bottom and copy the URL. Paste this URL in ‘Service URL’ text box in the vector tile connection options in QGIS.

11. Go back to the ArcGIS Online item page for the tile service and click on the ‘View Style’ button. You will be taken to a page with a bunch of plain text. Copy the URL of this page and paste it into the ‘Style URL’ text box in the vector tile connection options in QGIS.

12. In the vector tile connection options in QGIS, under ‘Authentication’, click ‘Basic’. Enter in the username and password for your ArcGIS Online account. The options should looks something like this. Click ‘OK’. And bingo!! You’re customized vector tile layer should have been added to QGIS!

A little time consuming, a little roundabout, but much easier then trying to recreate the basemaps that ESRI makes available and they really do make some good ones. Let me know if I can clarify anything.

As answered in the comments, you can't change a basemap. I often find basemaps using the SASplanet software, which is free software (download in the official page) and you can save the maps as a raster file to use it in your favourite GIS. There is plenty of options for different kind of maps so you might find something suitable for your needs. The picture just shows the sas planet menu for choosing the map sources.

Though you can download any map to your drive, some of them might be protected by a license, so make sure you know the limitations of what you use.