After fixing and upgrading my recently acquired 50 $ Microprofessor MPF-1 with a blue LED display (which turned out to be a bigger project than I thought!) I still needed to install the TinyBASIC, as the original MPF-1 only came with the monitor - in this case, a single 2716 EPROM in socket U6. TinyBASIC was then available as an upgrade EPROM for socket U7 - this would either be a 2516 or 2716 EPROM. These are still DIP24 sockets. 

You can see the original, standard MPF-1 with monitor in U6 and TinyBASIC in U7 here:
http://xjd0zipgwho4za58.myfritz.net:10381/Museum/MULTITECH-MPF-1.html

Only the later MPF-1B revisions changed these socket to DIP28, and a 2732 was then used to house both the monitor as well as TinyBASIC. U7 was left unpopulated on the 1B. Instead, U7 can be used for user programs, or for additional SRAM, by setting the J1 jumper (see below).

These two revisions hence had BASIC in different memory ranges - from 0x0800 - 0x0fff on the 1B, and from 0x2000 - 0x27ff on the 1, given that this is the memory range into which U7 is mapped into.

Unfortunately, the 2 KB U7 TinyBASIC from 0x2000 - 0x27ff was nowhere to be found on the usual internet sources of MPF ROM images (e.g., https://electrickery.hosting.philpem.me.uk/comp/mpf1/doc/) So I had to look for a different solution if I wanted to use TinyBASIC: 

Now, 2732 EPROMs come as both DIP 28 and DIP 24 versions; the MPF-1 uses DIP 24 for its U6 socket, and the MPF-1B uses a DIP 28 socket for U6. I hence decided to try the original MPF-1B 4 KB Monitor + TinyBASIC ROM image on the MPF-1, and programmed a DIP 24 2732.

Unfortunately, the MPF-1 didn't boot with the DIP 24 2732. I hence consulted the manual and found that it lists the 2516 as well as the 2532 as supported EPROMs for U6. Which is strange, given that my MPF-1 actually came with a 2716 in U6 - but it definitely did not like the 2732. However, the mentions of the 2532 in the manual encouraged me to try again, this time with a 2532. 

Even though I had some 2532 in my parts bin, I was actually not able to program one... as my EPROM programmer only supports 27xxx EPROMs. Hence, I decided to try with one of these 25xx <-> 27xx EPROM adapters; these work bidirectionally, so you can either use a 27xx EPROM and use it as a 25xx, or vice versa. As soon as I had the 2732 in the adapter, now acting as a 2532, the MPF-1 worked out of the box! It is now, by all means and purposes, equivalent to an MPF-1B, and I can use TinyBASIC and the monitor: 

You can get these adapters on Ebay.

Now, given that I had both the Monitor and TinyBASIC in U6, I still had U7 available - I can't leave a socket unpopulated, so what should I put there? Another EPROM? U7 can be configured for SRAM as well as for EPROM use. I opted for more SRAM - another 6116 SRAM would give me full 4 KBs of RAM, from 0x1800 to 0x27ff!

The J1 jumper modification requires cutting the default jumper traces for the vias / holes for J1, and then soldering in a pin header to accommodate "real" physical jumpers like in the picture. Next, for U7 to support the 6116 SRAM, the jumpers need to be set as follows - 1-2 4-5 6-7: